#### 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)

Done