Publications
2018

(2018) Journal of High Energy Physics. 2018, 1, 8. Abstract
In the search for QFT’s that admit boundstates, we reinvestigate the two dimensional GrossNeveu model, but with massive fermions. By computing the selfenergy for the auxiliary boundstate field and the effective potential, we show that there are no bound states around the lowest minimum, but there is a metastable bound state around the other minimum, a local one. The latter decays by tunneling. We determine the dependence of its lifetime on the fermion mass and coupling constant.
2014

(2014) Journal of High Energy Physics. 2014, 12, 165. Abstract
Abstract: In a previous paper [1], we analyzed the theory of massive fermions in the fundamental representation coupled to a U(N) ChernSimons gauge theory in three dimensions at level K. It was done in the large N , large K limits where (Formula presented.) was kept fixed. Among other results, we showed there that there are no high mass “quark antiquark” bound states. Here we show that there are no bound states at all.
2013

(2013) Journal of High Energy Physics. 2013, 12, 91. Abstract
We analyze the theory of massive fermions in the fundamental representation coupled to a U(N) ChernSimons gauge theory at level K. It is done in the large N, large K limits where λ = N/K is kept fixed. Following [1] we obtain the solution of a SchwingerDyson equation for the two point function, the exact expression for the fermion propagator and the partition function at finite temperature. We prove that in the large K limit there exists an infinite set of classically conserved high spin currents also when a mass is introduced, breaking the conformal invariance. In analogy to the seminal work of 't Hooft on two dimensional QCD, we write down a BetheSalpeter equation for the wave function of a "quark antiquark" bound state. We show that unlike the two dimensional QCD case, the three dimensional ChernSimons theory does not admit a confining spectrum.

(2013) Journal of High Energy Physics. 2013, 8, 96. Abstract
Recent observations by Belle and BESIII of charged quarkoniumlike resonances give new stimulus for theoretical investigation of exotic hadrons in general and heavy tetraquarks in particular. We use QED_{2}, a confining theory, as a model for the masses and decays of tetraquarks. Here we discuss the states (QQ̄qq̄) and (QQ̄qq̄) (and its antiparticle), where Q and q are two fermion flavors with masses M and m, so that M >m. Wethendiscussdecaymodesofthesestatesinto (QQ̄), (qq̄), (Qq̄), (Q̄q). Itturns out that (QQ̄qq̄) is stable, while (QQ̄qq̄) is not.
2006

(2006) Nuclear Physics B  Proceedings Supplements. 161, SPEC. ISS., p. 27 Abstract
We consider a "onecurrent" state obtained by application of a colour current on the "adjoint" vacuum in QCD _{2} with quarks in the fundamental representation. The quarks are taken to be massless. The theory on the lightfront can be "currentised" namely formulated in terms of currents only. The adjoint vacuum is obtained by applying a current derivative at zero momentum on the singlet vacuum. In general, the "onecurrent" states are not eigenstates of M ^{2} = 2 P ^{+} P ^{}, except in the large N _{f} limit. Problems with infrared regularisations are pointed out. Connection to fermionic structure is made. This talk is based on the paper of Ref. [A. Abrashkin, Y. Frishman and J. Sonnenschein, Nucl. Phys. B 703 (2004) 320, arXiv:hepth/0405165] by the same authors.
2005

(2005) Journal of High Energy Physics. 8, p. 20772088 Abstract
Twodimensional QCD has often been used as a laboratory for studying the full fourdimensional theory, providing, for example, an explicit realization of baryons as solitons. We review aspects of conventional baryons in twodimensional QCD, including the classical and quantum contributions to their masses. We then discuss the spectrum of exotic baryons in twodimensional QCD, commenting on the solitonic radius inferred from the excitation spectrum as well as the twodimensional version of the GoldbergerTreiman relation relating meson couplings to current matrix elements. Our treatment of twodimensional QCD, via the semiclassical quantization of collective coordinates, is consistent with chiralsoliton approaches to normal and exotic baryons in four dimensions, but is not able to resolve all the issues arising in fourdimensional models.
2004

(2004) Nuclear Physics B. 703, 12, p. 320332 Abstract
We consider a "one current" state, which is obtained by the application of a color current on the "adjoint" vacuum. This is done in QCD_{2}, with the underlying quarks in the fundamental representation. The quarks are taken to be massless, in which case the theory on the lightfront can be "currentized", namely, formulated in terms of currents only. The adjoint vacuum is shown to be the application of a current derivative, at zero momentum, on the singlet vacuum. We apply the operator M^{2}=2P^{+} P^{} on these states and find that in general they are not eigenstates of M^{2} apart from the large N_{f} limit. Problems with infrared regularizations are pointed out. We discuss the fermionic structure of these states.
2003

(2003) Physics Letters B. 566, 34, p. 201206 Abstract
Extending earlier work on strongcoupling mesonbaryon scattering in QCD_{2}, we derive the effective mesonbaryon action for any value of the coupling constant, in the largeN_{c} limit. Colour degrees of freedom play an important role, and we show that mesonbaryon scattering can be formulated as a relativistic potential problem. We distinguish two cases that are nontrivial for unequal quark masses, and present the resulting equations for mesonbaryon scattering amplitudes.

(2003) Nuclear Physics B  Proceedings Supplements. 117, SUPPL. 1, p. 391393 Abstract
Extending previous works on the spectrum of QCD_{2}, we now investigate the 2D analogue of mesonbaryon scattering. We use semiclassical methods, perturbing around classical soliton solutions. In the case of one flavor, we find that the effective potential is reflectionless. In the case of several flavors, the method yields a potential which depends on the momentum of the incoming particle. In this case there is both transmission and reflection. In both cases no resonances appear.
2002

(2002) Physics Letters B. 541, 34, p. 273280 Abstract
Extending previous works on the spectrum of QCD_{2}, we now investigate the 2D analogue of mesonbaryon scattering. We use semiclassical methods, perturbing around classical soliton solutions. We start with the Abelian case, corresponding to one flavor, and find that in this case the effective potential is reflectionless. We obtain an explicit expression for the forward phase shift. In the nonAbelian case of several flavors, the method yields a potential which depends on the momentum of the incoming particle. In this case there is both transmission and reflection. In both cases no resonances appear. As a byproduct, we derive the general conditions for a 2D scalar quantum field theoretical action to yield a reflectionless effective potential when one expands in small fluctuations about the classical solution.
2001

(2001) Nuclear Physics B. 596, 12, p. 459470 Abstract
We discuss the spectra of multiflavor massless QCD_{2}. An approximation in which the Hilbert space is truncated to two currents states is used. We write down a 't Hooft like equation for the wave function of the two currents states. We solve this equation for the lowest massive state and find an excellent agreement with the DLCQ results. In addition, the 't Hooft model and the large N_{f} limit spectra are rederived by using a description in terms of currents.
1999

(1999) International Journal of Modern Physics A. 14, 16, p. 24752493 Abstract
We review and elaborate on properties of the string tension in twodimensional gauge theories. The first model we consider is massive QED in the m ≪ e limit. We evaluate the leading string tension both in the fermionic and bosonized descriptions. We discuss the nexttoleading corrections in m/e. The nexttoleading terms in the long distance behavior of the quarkantiquark potential, are evaluated in a certain region of external versus dynamical charges. The finite temperature behavior is also determined. In QCD_{2} we review the results for the string tension of quarks in cases with dynamical quarks in the fundamental, adjoint, symmetric and antisymmetric representations. The screening nature of SYM_{2} is rederived.

(1999) Physics Letters B. 449, 12, p. 7680 Abstract
We show that the string tension in Script N sign = 1 twodimensional super YangMills theory vanishes independently of the representation of the quark antiquark external source. We argue that this result persists in SQCD_{2} and in twodimensional gauge theories with extended supersymmetry or in chiral invariant models with at least one massless dynamical fermion. We also compute the string tension for the massive Schwinger model, as a demonstration of the method of the calculation.

(1999) Nuclear Physics B. 537, 13, p. 503515 Abstract
Massless QCD_{2} is dominated by classical configurations in the largeN_{f} limit. We use this observation to study the theory by finding solutions to equations of motion, which are the nonabelian generalization of the Schwinger equation. We find that the spectrum consists of massive mesons with M^{2} = e^{2}N_{f}/2π, which correspond to abelian solutions. We generalize previously discovered nonabelian solutions and discuss their interpretation. We prove a nogo theorem ruling out the existence of soliton solutions. Thus the semiclassical approximation shows no baryons in the case of massless quarks, a result derived before in the strongcoupling limit only.
1998

(1998) Physical review letters. 80, 3, p. 430433 Abstract
We compute the string tension in massive QCD_{2}It is shown that the string tension vanishes when the mass of the dynamical quark is zero, with no dependence on the representations of the dynamical or of the external charges. When a small mass(m≪e)is added, a tension appears and we calculate its value as a function of the representations.
1997

(1997) Nuclear Physics B. 496, 12, p. 285301 Abstract
We analyze the question of screening versus confinement in bosonized massless QCD in two dimensions. We deduce the screening behavior of massless SU(N_{c}) QCD with flavored fundamental fermions and fermions in the adjoint representation. This is done by computing the potential between external quarks as well as by bosonizing also the external sources and analyzing the states of the combined system. We write down novel "nonAbelian Schwinger like" solutions of the equations of motion, compute their masses and argue that an exchange of massive modes of this type is associated with the screening mechanism.

(1997) Physical review D. 55, 7, p. 39944000 Abstract
We calculate in twodimensional QCD (QCD[Formula presented] the ratios of baryonic matrix elements of [Formula presented] and [Formula presented] fourfermion operators, with a view to understanding better the mechanism of [Formula presented] enhancement in QCD[Formula presented]. We find relatively small suppressions of both the scalarscalar and vectorvector [Formula presented] fourfermion operators. We discuss the possible implications of these results, in view of a suggestion that gluon condensation may be an important contributing factor in the [Formula presented] enhancement seen in QCD[Formula presented]. At the technical level, our calculation of the vectorvector operator matrix element requires a treatment of the time dependence of the QCD[Formula presented] soliton which had not been developed in previous phenomenological calculations within this model.
1994

(1994) Nuclear Physics B. 429, 1, p. 7589 Abstract
It is shown that in a formulation of YangMills theory in two dimensions in terms of A = i f^{ 1} ∂ f, over(A, ) = i over(f, ) over(∂, ) over(f, )^{ 1} with f (z, over(z, )), over(f, ) (z, over(z, )) ∈ [S U (N_{C})]^{c} the complexification of SU(N_{C}), reveals certain subtleties. "Physical" massive color singlet states seem to exist. When coupled to N_{F} quarks the coupling constant is renormalized in such a way that it vanishes for the pure YangMills case. This renders the above states massless and unphysical. In the abelian case, on the other hand, the known results of the Schwinger model are reproduced with no need of such a renormalization. The massless QCD_{2} theory is analyzed in similar terms and peculiar massive states appear, with a mass of e_{c} sqrt(N_{F} / 2 π) .

(1994) Nuclear Physics B. 424, 1, p. 317 Abstract
We derive an effective lowenergy action for QCD in 4 dimensions. The low energy dynamics is described by chiral fields transforming nontrivially under both color and flavor. We use the method of anomaly integration from the QCD action. The solitons of the theory have the quantum numbers of quarks. They are expected to be the constituent quarks of hadrons. In two dimensions our result is exact, namely the bosonic gauged action of WZW.
1993

(1993) Physics ReportsReview Section Of Physics Letters. 223, 6, p. 309348 Abstract
Quantum Chromodynamics (QCD) is believed to describe the strong interactions. In the asymptotic domain of large momenta, improved perturbation theory describes phenomena by use of pointlike quarks and gluons. But the spectrum and wave functions are in the nonperturbative domain, for which not much can be done analytically in four dimensions. In order to develop analytical methods physicists turned to simpler models, like QCD_{2}, the theory in one space and one time dimensions. This review is devoted to the application of bosonization techniques to twodimensional QCD. We start with a description of the "abelian bosonization". The methods of the abelian bosonization are applied to several examples like the Thirring model, the Schwinger model and QCD_{2}, The failure of this scheme to handle flavored fermions is explained. Witten's nonabelian bosonization rules are summarized including the generalization to the case of fermions with color and flavor degrees of freedom. We discuss in detail the bosonic version of the mass bilinear of coloredflavored fermions in various schemes. The color group is gauged and the full bosonized version of massive multiflavor QCD_{2} is written down. The strong coupling limit is taken in the "product scheme" and then in the U(N_{F} × N_{C}) scheme. Once the multiflavor QCD_{2} action in the interesting region of the low energies is written down, we extract the semiclassical lowlying baryonic spectrum. First, classical soliton solutions the bosonic action are derived. Quantizing the flavor space around those classical solutions produces the masses as well as the flavor properties of the twodimensional baryons. In addition, lowlying multibaryonic solutions are presented, as well as wave functions and matrix elements of interest, like qq̄ content.

(1993) Journal of Physics A: Mathematical and General. 26, 2, p. 301312 017. Abstract
Fieldtheoretic models for fields taking values in quantum groups are investigated. First the authors consider the SU_{q}(2) sigma model (q real) expressed in terms of basic notions of noncommutative differential geometry. They discuss the case in which the sigma model fields are represented as products of conventional sigma fields and of the coordinateindependent algebra. An explicit example is provided by the U_{q}(2) sigma model with q^{N}=1, in which case quantum matrices U_{q}(2) are realized as 2N*2N unitary matrices. Open problems are pointed out.
1992

(1992) Nuclear Physics B. 382, 2, p. 189212 Abstract
We exhibit static solutions of multiflavour QCD in two dimensions that have the quantum numbers of baryons and mesons, constructed out of quark and antiquark solitons. In isolation the latter solitons have infinite energy, corresponding to the presence of a string carrying the nonsinglet colour flux off to spatial infinity. When N_{c} solitons of this type are combined, a static, finiteenergy, colour singlet solution is formed, corresponding to a baryon. Similarly, static meson solutions are formed out of a soliton and an antisoliton of different flavours. The stability of the mesons against annihilation is ensured by flavour conservation. The static solutions exist only when the fundamental fields of the bosonized lagrangian belong to U(N_{c} × N_{f}) rather than to SU(N_{c}) × U(N_{f}). Discussion of flavoursymmetry breaking requires a careful treatment of the normalordering ambiguity. Our results can be viewed as a derivation of the constituent quark model in QCD_{2}, allowing a detailed study of constituent mass generation and of the heavyquark symmetry.
1991

(1991) Physics Letters B. 272, 34, p. 333338 Abstract
We exhibit soliton solutions of QCD in two dimensions that have the quantum numbers of quarks. They exist only for quarks heavier than the dimensional gauge coupling, and have infinite energy, corresponding to the presence of a string carrying the nonsinglet color flux off to spatial infinity. The quark solitons also disappear at finite temperature, as the temperature, as the temperaturedependent effective quark mass is reduced in the approach to the quark/hadron phase transition.
1990

(1990) Nuclear Physics B. 344, 2, p. 393400 Abstract
We write down the baryon wave functions in QCD_{2} in the strongcoupling semiclassical approximation. These wave functions are expressed as polynomials in z_{i} and z_{i}^{*, i = 1, ..., N}, where N is the number of flavors. The znumber minus the z^{*}number in the wave function is constrained to be equal to the number of colors, N_{c}. The strange quark content is calculated for some of these states.

(1990) Nuclear Physics B. 331, 3, p. 781785 Abstract
We derive explicit expressions for the masses and the binding energies of kbaryon states in twodimensional (one space and one time) quantum chromodynamics (QCD(2)). The expressions are given using the parameters n_{1}, n_{2}, ..., n_{Nf1} which characterize the representation of SU(N_{f}), where N_{f} is the number of flavours, in terms of its Young tableau description. We find that the difference between the mass of the kbaryon state and the sum of masses of any combination of its constituents is independent of the value N_{f} (i.e. the number of flavours)(up to the overall mass scale M). These results hold within a certain bosonized form of QCD(2) and within the strong coupling limit of (G/m) → ∞, where G is the gauge coupling constant and m the quark mass.
1989

(1989) Nuclear Physics B. 328, 2, p. 375386 Abstract
We find multibaryon states in twodimensional quantum chromodynamics. We show that to bind two baryons the model must involve at least seven flavours. All calculations are performed in the strong coupling limit and the semiclassical approximation is employed in the derivation of the results. We briefly comment on the properties of the derived states.
1988

(1988) Nuclear Physics B. 301, 2, p. 346356 Abstract
We present bosonic actions which are equivalent to various chiral fermion theories. For the case of one chiral fermion coupled to an abelian gauge field, we present two bosonized actions, one corresponding to regularizing in the vector conserving scheme and the other in the leftright scheme. We then propose an action for the nonabelian bosonization of Weyl fermions which is a WZW action coupled to a fixed curved background. The chiral WZW action is then coupled to nonabelian gauge fields. We derive the anomalies of the axial current (in the vector conserving scheme) and the leftright currents (in the leftright regularization scheme), both for the abelian and nonabelian bosonized actions. The expressions for the anomalies are identical to those derived in the corresponding fermionic theories.
1987

(1987) Nuclear Physics B. 294, C, p. 801812 Abstract
The WZW action on SU(N_{C}) × SU(N_{F}) × U(1) group manifold was proposed as the bosonized theory of free colored and flavored Dirac fermions. Here difficulties are encountered in finding the fermion mass bilinears in terms of boson variables. We thus try an alternative approach using WZW theory on U(N_{C} × N_{F}) group manifold, where there is no problem with the mass bilinears. After gauging the color we obtain the bosonized form of multiflavor QCD_{2}. The strong coupling limit is then taken and the low energy effective action is obtained. We then show that this action, though different from the one we got in the past from the "old" prescription, describes the same low lying semiclassical baryonic spectrum.

(1987) Nuclear Physics B. 283, C, p. 365380 Abstract
A generalization of Witten's nonabelian bosonization to gauge theories can be used to derive an effective action for the strong coupling limit of massive multiflavor QCD in 1 + 1 dimensions. Here we analyze this action and obtain the semiclassical spectrum of soliton solutions corresponding to the twodimensional baryons. The possible flavor representations of the baryons are found and compared to quark model predictions. We give a formula for the masses of the baryons in terms of their group properties and the quark mass.
1986

(1986) Nuclear Physics B. 273, 1, p. 93108 Abstract
Simple and tractable examples of abelian and nonabelian gauge systems with global anomalies are presented in quantum mechanics. Explicit calculations are done both in the pathintegral and hamiltonian formalism. Algebraic criteria are given for the existence of global gauge anomalies. These criteria are applied for every gauge group and many representations. The inconsistency of theories with a global gauge anomaly is discussed.

(1986) Physics Letters B. 167, 3, p. 347350 Abstract
To leading order in α_{s}(Q^{2}) conformal symmetry specifies the eigensolutions of the evolution equation for meson distribution amplitudes, the wavefunctions which control largemomentumtransfer exclusive mesonic processes in QCD. We find that at next to leading order, the eigensolutions in various field theories depend on the regularization scheme, even for zero βfunction. This is contrary to the expectations of conformal symmetry.

(1986) Physical review D. 33, 7, p. 18811893 Abstract
We present a systematic analysis in perturbative quantum chromodynamics and other renormalizable theories of higherorder corrections to quark distribution amplitudes for flavornonsinglet mesons, the wave functions which control leadingtwist exclusive processes. In particular, we investigate the utility of residual conformal symmetry near the light cone. We find that beyond leading order the eigensolutions of the evolution equations are regulatordependent in renormalizable theories. In a specific calculation for 3 theory in six dimensions to two loops, we find that the eigensolutions obey conformal symmetry using dimensional regularization for the subset of diagrams which do not contribute to the function, but conformal symmetry is broken using PauliVillars regularization. A comparison with existing calculations of the twoloop kernel for gauge theory with =0 indicates that conformal symmetry does not hold beyond leading order in QCD in dimensional regularization.
1984

(1984) Physics Letters B. 141, 12, p. 7678 Abstract
We show directly the connection between two and fourdimensional soliton theories coupled to fermions, thus explaining the equality of their respective fractional charges. The dependence of these charges on the boundary conditions of the "half fermions" is also computed.
1983

(1983) Physics Letters B. 130, 12, p. 6668 Abstract
Noninteger charges on topological objects in the presence of fermions are further investigated. The connections with anomalous commutators is discussed. The reason for the identical results in two dimensional solitons and four dimensional monopoles is pointed out.

(1983) Nuclear Physics B. 218, 2, p. 445458 Abstract
The properties of topological objects with fractional charge are studied. We first transform to new variables, in terms of which the lowest order contribution gives the fractional charge. We then gauge that fractional charge. Effects of the θ angle in two dimensions are studied. In particular arbitrary periods may be obtained. Induced extra charge due to θ turns out to be proportional to trθ. C and P violations due to θ may be arbitrarily small in some cases.

(1983) Physics Letters B. 121, 23, p. 180182 Abstract
We present the bosonized hamiltonian for (QCD)_{2} with flavor. The bosonized theory has non local momentum dependent interactions. It is argued that the strong coupling static approximation is unacceptable.

(1983) Physical Review B. 27, 4, p. 25652568 Abstract
Charge fluctuations of solitons with arbitrary fractional fermion number in 1 + 1 dimensions are calculated, generalizing the result of Kivelson and Schrieffer for solitons with fermion number 1/2. The soliton charge is measured by a sampling function f(x) such that f(x)1 over a region of width L around the soliton and then falls to zero in a distance l. It is shown that vacuum fluctuations vanish as l1 for large l while the additional fluctuations due to the presence of a soliton vanish as either exp(Lξ) or exp(2Δ0L); ξ is the soliton width and Δ0 is the mass gap of a ground state. This result establishes that the fractional fermion charge is a welldefined observable.
1982

(1982) Physics Letters B. 109, 12, p. 3539 Abstract
Vector SU(N_{c}) gauge theories with n_{f} flavors in the fundamental representation are considered. We prove that if the persistent mass condition is assumed, the two anomaly equations are i dentical and flavor independent for n_{f}{slanted equal to or greaterthan} 3. Integer solutions exist only for n_{f}=2. The necessity of a separate discussion for 2≤n_{f}≤N_{c} is explained.
1981

(1981) Nuclear Physics B. 191, 2, p. 493510 Abstract
The ideas of tumbling and most attractive channel condensation are confronted in twodimensional chiral gauge theories. We first demonstrate how to perform a gaugeinvariant regularization. We then proceed to find exact results about the spectra in both abelian and nonabelian cases. These conflict with the predictions of tumbling and MAC.

(1981) Nuclear Physics B. 177, 1, p. 157171 Abstract
We show that the axial anomaly of threepoint functions of colour singlet currents in quark confining theories implies the presence of zeromass bound states in the physical spectrum. These can be either massless fermions or Goldstone bosons. This supplements an argument given by 't Hooft. We then show, for any number of colours (with more than two flavours), that Goldstone bosons actually follow. Various aspects of heavy quark decoupling are also discussed.

1980

(1980) Physics Letters B. 96, 34, p. 302304 Abstract
We investigate the use of various schemes (for the effective coupling constant) to obtain the asymptotic behavior of the physical quantities. In a simple model, with dimensional transmutation, it turns out that a scheme in which the effective coupling has a Landau pole is suitable for studying asymptotic behavior. Another scheme, in which no such pole occurs, can actually not be used to obtain the asymptotic behavior due to nonexpandability in small coupling.

(1980) Physics Letters B. 91, 2, p. 239244 Abstract
The operator product expansion, of appropriate products of quark fields, is used to find the anomalous dimensions which control the short distance behavior of hadronic wave functions. This behavior in turn controls the highQ^{2} limit of hadronic form factors. In particular, we relate each anomalous dimension of the nonsinglet structure functions to a corresponding logarithmic correction factor to the nominal α_{S}(Q^{2})/Q^{2} fall off of meson form factors. Unlike the case of deep inelastic leptonhadron scattering, the operator product necessary here involves extra terms which do not contribute to forward matrix elements.

(1980) Nuclear Physics B. 165, 1, p. 185188 Abstract
The general condition for the validity of the usual perturbation expansion, in gauges with copies, is given. This includes abelian and nonabelian cases. The condition is that the potentials of copies be "far" from each other.
1979

(1979) Nuclear Physics B. 148, 12, p. 9395 Abstract
A Minkowski space regularization in twodimensional nonAbelian SU(N) gauge theory in the N→∞ limit, is shown to yield the same fermion propagator as a recently proposed Euclidean space regularization. It is also shown that the difference between the above result and the result of the principal value regularization, is obtained by adding a term to the gluon propagator which satisfies the homogeneous equation. This indicates that the structure of the singlets is the same for all these regularization.

(1979) Physical review D. 19, 2, p. 540548 Abstract
The largeorder behavior of perturbation theory of φ4 theory in four dimensions in the presence of mass terms is estimated. A new scale comes into the coefficient functions. For mass m and order K this scale is mK.

(1979) Nuclear Physics B. 148, 12, p. 7492 Abstract
NonAbelian gauge theory of quarks and gluons with SU(n) symmetry, in onespace and onetime dimensions, is investigated in the largen limit. Special attention is given to the infrared regularization. The fermion propagator turns out to be cutoff independent. It is shown that in the n→∞ approximation, tachyons appear in the twopoint function of the scalar density for mass m=0 of the quarks. This is not the case when m≠0 with m→0 is taken. Thus m=0 is singular. It is also shown that the singlet vector current has a free twopoint function for m=0, which entails a consistency condition on bound state wave functions.
1978

(1978) Nuclear Physics B. 146, 1, p. 2028 Abstract
The effects of vacuum copies on perturbation theory are studied. The usual procedure of perturbation expansion around the zero copy leads to incorrect results in the Abelian case. However, in nonAbelian gauge theory the above usual procedure reproduces the correct perturbation series.
1977

(1977) Physical review. D, Particles and fields. 15, 8, p. 22752281 Abstract
It is shown that the standard infraredcutoff procedures are inconsistent with the general axial gauge in 't Hooft's twodimensional model of confinement.
1975

(1975) Physical review D. 11, 10, p. 30403045 Abstract
Spontaneous mass generation is discussed. General arguments are given for the case of two zeros of β, implying no mass generation between the zeros. This is used to question the 1N expansion in a fourfermion twodimensional model. General comments regarding dynamical mass and effective potential are also included.
1973

(1973) Physics Letters B. 46, 3, p. 439442 Abstract
Generalizations of the Thirring model to Fermi fields with U(n) symmetry are treated. When interactions quadratic in the SU(n) currents are introduced, scale invariance (with anomalous dimensions) is maintained only for values of the coupling g_{v}=0 or g_{v} = 4φ (n+1).

(1973) Physical review D. 7, 6, p. 16611668 Abstract
The relation between generalized scaling laws, or equivalently lightcone behavior of current commutators, and equaltime commutators is investigated. In particular, the finiteness of the CallanGross integrals over equaltime commutators does not imply Bjorken scaling. It can happen that W2 or even (1ν)W2 scales. Also, even in the cases of forward matrix elements, the correspondence between lightcone and shortdistance singularities is not onetoone in general. The various cases are investigated. Operator Schwinger terms and their relation to the longitudinal cross section are also discussed.

(1973) Physical review letters. 31, 2, p. 135138 Abstract
It is argued that lightcone dominance ideas are compatible with canonical scaling in the process ee+→hadrons+anything and a logarithmic increase in hadronic multiplicity.
1972

(1972) Physical review. D, Particles and fields. 6, 4, p. 9881007 Abstract
Exact expansions of operator products, in terms of cnumber functions singular on the light cone and regular operators, are exhibited explicitly in the Thirring model. For the products ψ1(x)ψ1†(x′) and ψ2(x) ψ2†(x′) of fermion fields the expansion reduces to one term only, with the cnumber function having a singularity on the light cone which depends on the coupling constant, and the regular operator depending only on the currents, which are free. The resulting formula allows one to calculate all Wightman functions in terms of current matrix elements and thereby provides a simple and complete solution to the Thirring model. The different charge sectors are realized as inequivalent irreducible representation spaces of the canonical current commutation relations, on which the charged field ψ acts as an intertwining operator.
1971

(1971) Annals of Physics. 66, 1, p. 373389 Abstract
The recently proposed expansion of products of local operators when their spacetime distance approaches the light cone is motivated and discussed. Attempts to prove the expansion from Wilson's short distance expansion are analyzed. Applications to processes involving currents in certain asymptotic domains are reviewed and difficulties are pointed out.

(1971) Physical review letters. 26, 13, p. 798801 Abstract
It is shown that lightcone dominance ideas apply to exclusive processes as well. These processes must include a photon of large virtual mass, as for example deep pion electroproduction. The method provides for a new general parametrization for amplitudes in the Bjorken limit. If correct, it will lend strong support to the ideas of lightcone expansions of operator products and provide a way to study the structure, at short distances, of the commutators of electromagnetic currents and strong sources.
1970

(1970) Physical review letters. 25, 14, p. 966969 Abstract
Consequences of the assumption that current commutators have powertype singularities near the light cone are derived. An extension of Wilson's shortdistance expansion of commutators is suggested for almost lightlike distances. Consequences for powertype singularities are derived for processes involving currents. Especially, generalized scaling laws are obtained for inelastic electronnucleon scattering. The connection with Regge behavior is discussed. An application to electronpositron annihilation into hadrons is also made.
1969

(1969) Physical review. 180, 5, p. 15561571 Abstract
Free fields of massless particles transforming covariantly under the Poincaré group are constructed. The allowed infinite and finitedimensional representations of the Lorentz group are obtained. The wave functions are calculated in these representations in various bases. The commutation rules are computed, and turn out to be nonlocal for any infinitedimensional fields. The transformation law of a certain irreducible infinitedimensional representation is shown to coincide, for its lowestspin component, with the usual, radiationgauge, vectorpotential transformation law, as already discovered by Bender.

(1969) Physical review letters. 22, 11, p. 572576 Abstract
It is shown that a class of theories, of which Sugawara's theory of currents and certain YangMills type theories are examples, possess a particular symmetry which is not, even approximately, present in the observed strong interactions. The symmetry would imply that all mesons and all massive fermions have partners with opposite parity and opposite charge conjugation.
1968

(1968) Physical Review. 170, 5, p. 13531359 Abstract
We show that Sugawara's theory of currents can be obtained as a formal limit of the massive YangMills theory. In this limit, g0→0 and m0→0 in such a way that m02g02=C, the constant appearing in Sugawara's theory. The limiting procedure is used to incorporate electromagnetism, the hypothesis of partially conserved axialvector current, and SU(3) breaking into the theory, retaining canonical structure for electromagnetism.

(1968) Physical review. 165, 5, p. 15551556 Abstract
Equations for the divergence of the vector and axialvector currents follow from the assumptions of Lorentz invariance, locality, the chiral SU(3)×SU(3) commutators between charges and charge densities, and the usual electromagnetic and weak Hamiltonians. The divergence conditions lead to derivations of the lowenergy meson theorems which do not involve Schwinger terms.

(1968) Physical review. 171, 5, p. 14421452 Abstract
We discuss the possibility of constructing, out of particle creation and destruction operators, local quantum fields that transform as representations of the homogeneous Lorentz group. Our immediate goal is to write down a consistent local quantum field theory which can simultaneously describe many particles with different masses and spins. In the case that the field is a finitedimensional irreducible Lorentz tensor, we are able to carry through our program with no restrictions on the masses considered as functions of the spin, provided the usual connection between spin and statistics is satisfied. However, when the field transforms as a unitary irreducible representation of the homogeneous Lorentz group (an infinitedimensional representation), the requirement of locality, along with the physical assumption that the masses are bounded below, m(j)am0>0, leads to the restriction that the masses are independent of the spin. This property is shown to hold when the transformation law of the field is taken to be an irreducible finitedimensional representation a unitary irreducible representation. The physical consequences of this result and possible methods for evading it are discussed. Finally, an Appendix is included, where the related problem of orthogonality properties of timelike solutions to infinitecomponent wave equations is examined. In particular, we show that when the solutions of such wave equations transform as unitary irreducible representations of the homogeneous Lorentz group, only the Majorana representations support a scalar product, which is orthogonal for different spins.
1967

(1967) Physical review. 156, 5, p. 16231624 Abstract
The dependence of spontaneous symmetry breaking on the representation is discussed. In case the usual symmetrybreaking condition is not realized, a modified condition may be found, which replaces the former in proofs of the Goldstone theorem.


(1967) Physical review. 159, 5, p. 14281430 Abstract
It is shown, directly from proper Lorentz invariance and a positive Hilbertspace metric, that the vacuum expectation value ã€̂ 0[j0(x),jk†(y)]0ã€‰ cannot vanish unless jμ(x)0ã€‰=jμ†(x)0ã€‰‰ 0. Neither locality nor KällénLehmanntype representations are needed. The same is demonstrated for ã€̂0[Skl(x),S0m†(y) ]0ã€‰, for any antisymmetric tensor Sμν. The explicit dependence of jμ and Sμν on the fields with which they interact is an immediate consequence in our approach. Similarly, it is easy to show that χ(x), χ(x)=̂,μjμ(x), does not commute with j0†(y) for y0=x0, unless χ(x)0ã€‰=χ†(x) ã€‰‰0.

1966


Average charge distributions in systems of nucleons and pions(1966) Proceedings of the 9th International Conference on Cosmic Rays, London, September 1965. Bombay: . Vol. 2. p. 946949 Abstract
Closed expressions are derived for the average charge distributions in systems of nucleons and pions with given total isotopic spin and charge. It is also shown that in nucleonnucleus collisions with multiple pion production, on the average one third of the pions produced are neutral and the difference between the numbers of positive and negative pions tends to +1/2 or 1/ for proton or neutronnucleus collisions, respectively, as the total number of produced pions tends to infinity

(1966) Physical review. 143, 4, p. 11351138 Abstract
Closed formulas are given for the relativistic helicity eigenstates of a wave function for any spin. Helicity amplitudes for the production of higher spin particles are then computed and brought to a simple form for pion and vectormeson exchange.

1965

(1965) Physical review. 138, 6B, p. B1450B1456 Abstract
The asymptotic behavior of the vertex function Γμ(p+l,pl) for high p(p2→) is found for massless barefermion electrodynamics. Those terms which contribute to the leading terms of Z31 are calculated by a nonperturbative method. This leads to Z3=0.

(1965) Journal of Mathematical Physics. 6, 12, p. 18551856 Abstract
A simple connection between the radial Schrödinger equation for the bound states of a hydrogen atom with angular momentum ι and that of an isotropic harmonic oscillator of even dimension from 2 to 4ι + 4 is noted. The case of highest dimensionality 4ι + 4 is shown to lead in a very simple way to the energy levels and degeneracies of the hydrogen atom, once the energy levels of a onedimensional harmonic oscillator are known.

(1965) Physical review. 140, 4B, p. B1151B1156 Abstract
A general method is given for calculating the exact form of the helicity eigenstates of a wave function for any spin. Explicit expressions of the wave functions for spin S=1,32,2, and 52 are listed. Examples of helicity amplitudes for the production of S=32+ and S=52+ isobars in protonproton scattering are computed.
1964


Derivation of the muon charge ratio using a simple pionproduction model(1964) Proceedings of the International Conference on Cosmic Rays, Jaipur, December 214, 1963 / edited by R.R. Daniel ... [et al.] ; under the auspices of the International Union of Pure and Applied Physics, and the Department of Atomic Energy, Government of In. Bombay: . Vol. 6. p. 4550 Abstract
The observed vertical meson (ut)/() ratio at sea level was previously explained by several collision models, but these models were unsuccessful in some respects. Another modification of the simple mesons(7) only model is considered. The values so obtained agree very well with observed charge ratio values. The experimental and calculated charge ratios are tabulated and compared.