לוח שנה משולב

: The Wheeler DeWitt equation is the statement that theories of gravity are topological in the bulk and only have boundary DOF. This fits with the Covariant entropy conjecture, which associates an areas worth of DOF to the boundary of a causal diamond. For nested diamonds it implies that the algebra of operators on the smaller one be a proper subalgebra of that on the larger one. Jacobson showed, conversely, that the area law implies Einstein's equations (except for the c.c., which Banks and Fischler argued was an asymptotic boundary condition). In Minkowski space, the maximal causal diamond is Penrose's conformal boundary. Traditionally we deal with this by introducing an S matrix, but this only works in perturbation theory because of the inevitable existence of states with arbitrary numbers of arbitrarily soft gravitons (even when there are no IR divergences). Instead we introduce an algebra of densities describing the flow of quantum numbers out to null infinity. The simplest of these are the commuting BMS local translations, which one can diagonalize. The joint spectrum of the past and future BMS generators defines a null cone, and all other currents may be thought of as generalized functions on this cone. The algebra must include helicity raising operators and the simplest way to introduce them (perhaps the only consistent way) is to write a generalization of the Awada Gibbons Shaw supersymmetric BMS algebra. One must define Sterman Weinberg jet representations of this algebra, which reveal that particle energy is related to constraints on the density degrees of freedom. Retreating from infinity to a finite causal diamond, the current algebra is cutoff by cutting off the spectrum of the Dirac operator on the holographic screen - a UV/IR correspondence reminiscent of that in AdS/CFT.