Gauge Fixing in the Chain by Chain Method

TL;DR

The paper introduces a 'chain by chain' method for gauge fixing in Hamiltonian systems with constraints, providing an efficient and consistent approach by focusing on conjugate conditions to the last elements of first class chains.

Contribution

It presents a novel gauge fixing procedure using the chain by chain method, simplifying the process for arbitrary constrained Hamiltonian systems.

Findings

Gauge fixing conditions can be set using conjugate conditions to last elements of first class chains.

Remaining conditions are derived from consistency requirements.

The method ensures an economical and consistent gauge fixing process.

Abstract

In a recent work we showed that for a Hamiltonian system with constraints, the set of constraints can be investigated in first and second class constraint chains. We show here that using this "chain by chain" method for an arbitrary system one can fix the gauges in the most economical and consistent way. We show that it is enough to assume some gauge fixing conditions conjugate to last elements of first class chains. The remaining necessary conditions would emerge from consistency conditions.