Poincar\'{e} gauge symmetries, hamiltonian symmetries and trivial gauge transformations

TL;DR

This paper establishes a method to relate Hamiltonian gauge symmetries to Poincaré symmetries in constrained systems, showing their equivalence up to trivial transformations.

Contribution

It introduces a procedure to derive Poincaré symmetries from Hamiltonian gauge symmetries using Noether identities, clarifying their relationship.

Findings

Poincaré and Hamiltonian gauge symmetries are equivalent modulo trivial transformations.

A systematic map between gauge parameters is constructed.

The approach resolves a longstanding problem in gauge symmetry analysis.

Abstract

We resolve a problem of finding the Poincare symmetries from hamiltonian gauge symmetries constructed through a canonical procedure of handling constrained systems. Through the use of Noether identities corresponding to the symmetries, we motivate a procedure of finding the map between the hamiltonian and Poincare gauge parameters. Using this map, we show that the Poincare and hamiltonian gauge symmetries are equivalent, modulo trivial gauge transformations.