Alladi Ramakrishnan Hall

Equations of Motion as Quantum Constraints: Super Selection Rules, Ward Identities

A P Balachandran

IMSc

In 1952, Peierls formulated the Peierls bracket , a spacetime approach
to quantisation. It depends on the causal features of equations of motion
and is manifestly covariant. In this talk, the Peierls bracket is used to
formulate equations of motion in Q.E.D. as quantum constraints. They are
first class in the sense of Dirac and commute with local observables. They
also generate *spacetime dependent* gauge transformations and hence
formulate the covariant Gauss law without appeal to spatial slices. Super
selection rules are formulated by enlarging the space of relevant test
functions and it is found that the BMS group acts non-trivially as an
automorphism group on the super selection algebra . It is therefore
spontaneously broken.The well-known result that charge labels super
selection sectors emerges without any appeal to Lorentz invariance :
quantum treatment of equations of motion and causality imply this
result.The momentum space version of the Sky group of Balachandran and
Vaidya also emerges as the generalised super selection group. The
operators which generate them, just like the charge operator, are conserved.

( Work with Manolo Asorey and Beppe Marmo)