Normal forms and gauge symmetries of local dynamics

TL;DR

This paper introduces a systematic method for deriving gauge symmetries in general local dynamics, extending traditional algorithms beyond variational systems and enabling BRST embedding without variational principles.

Contribution

It develops a unified procedure for gauge symmetry derivation applicable to both variational and non-variational equations of motion, generalizing the Dirac-Bergmann algorithm.

Findings

The procedure reduces to the Dirac-Bergmann algorithm for variational systems.

It identifies counterparts of constraints without Poisson structures.

The reformulation in involutive normal form allows BRST embedding without variational principles.

Abstract

A systematic procedure is proposed for deriving all the gauge symmetries of the general, not necessarily variational, equations of motion. For the variational equations, this procedure reduces to the Dirac-Bergmann algorithm for the constrained Hamiltonian systems with certain extension: it remains applicable beyond the scope of Dirac's conjecture. Even though no pairing exists between the constraints and the gauge symmetry generators in general non-variational dynamics, certain counterparts still can be identified of the first- and second-class constraints without appealing to any Poisson structure. It is shown that the general local gauge dynamics can be equivalently reformulated in the involutive normal form. The last form of dynamics always admits the BRST embedding, which does not require the classical equations to follow from any variational principle.