The main line is in the area of non-abelian gauge theories, which within the standard
model describe strong, electromagnetic and weak interactions as observed in Nature.
A particular aspect is that of deep-inelastic scattering of electrons, muons and
neutrinos off hadrons. In that connection, we developed the structure of operator products,
in particular currents, at almost light-like distances (see 1).
This expansion is a standard tool in investigating scattering experiments as above.
The leading experimentalists in those experiments, Friedman and Kendall and Taylor,
received a Nobel prize in 1990.
Another aspect is that of describing energy and momentum in terms of products of currents.
We generalized the Sugawara construction to the non-abelian case, where the
normal ordering effects had to be taken into account, obtaining the second Casimir dependence
in the coefficients.
These expressions are now being used in Conformal Field Theory as well as in
String Theory (see 2).
To obtain the spectrum and various other properties of states, strong coupling methods
have to be developed. These we did in two dimensional models (see 3 for review).
Issues of confinement and screening in non-abelian gauge theories have also been addressed.
In particular, the string tension was computed in various cases in model theories in two dimensions.
We have also computed the effective potential for meson-baryon scattering,
and then the transmission and reflection amplitudes (see papers in 4).
We have a book, together with Jacob Sonnenschein, on various non-perturbative methods in field theory,
starting from one space dimension and going to three space dimensions (see 5),
published by Cambridge University Press.
- Y. Frishman
"Scale invariance and current commutators near the light cone'', Phys. Rev. Lett. Vol. 25, P. 966 (1970).
- R. Dashen and Y. Frishman
"Four-fermion interactions and scale invariance'', Phys. Rev. vol. D11, P. 2781 (1975).
- Y. Frishman and J. Sonnenschein
"Bosonization and QCD in Two Dimensions'', Physics Reports, vol. 223, No 6 (1993).
- See papers
- Yitzhak Frishman and Jacob Sonnenschein
"Non-Perturbative Field Theory -- From two dimensional conformal field theory to QCD in four dimensions", Cambridge University Press, Apr 2010, 436 pages.
Summary note for the book is in e-Print: arXiv:1004.4859 [hep-th].