Equations of Motion as Constraints: Superselection Rules, Ward Identities

2021, May 13
M. Asorey, A.P. Balachandran, F. Lizzi, G. Marmo
JHEP 1703 (2017) 136
The meaning of local observables is poorly understood in gauge theories, not to
speak of quantum gravity. As a step towards a better understanding we study asymptotic
(infrared) transformations in local quantum physics. Our observables are smeared by test
functions, at rst vanishing at infinity. In this context we show that the equations of motion
can be seen as constraints, which generate a group, the group of space and time dependent
gauge transformations. This is one of the main points of the paper. Infrared nontrivial
e ects are captured allowing test functions which do not vanish at infinity. These extended
operators generate a larger group. The quotient of the two groups generate superselection
sectors, which differentiate different infrared sectors. The BMS group changes the super-
selection sector, a result long known for its Lorentz subgroup. It is hence spontaneously
broken. Ward identities implied by the gauge invariance of the S-matrix generalize the
standard results and lead to charge conservation and low energy theorems. Their validity
does not require Lorentz invariance.