Canonical brackets from continuous symmetries: Abelian 2-form gauge theory

TL;DR

This paper derives canonical (anti-)commutation relations for a 4D Abelian 2-form gauge theory using continuous symmetry transformations within the BRST formalism, revealing consistent relations across all symmetries.

Contribution

It introduces a method to obtain canonical (anti-)commutation relations from continuous symmetries in a 4D Abelian 2-form gauge theory, demonstrating their consistency.

Findings

All six continuous symmetries yield identical non-vanishing (anti-)commutators.

The approach confirms the symmetry-based derivation of canonical relations.

The method applies within the BRST formalism to higher-form gauge theories.

Abstract

We derive the canonical (anti-)commutation relations amongst the creation and annihilation operators of the various basic fields, present in the four (3 + 1)-dimensional (4D) free Abelian 2-from gauge theory, with the help of continuous symmetry transformations within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism. We show that all the six continuous symmetries of the theory lead to the exactly the same non-vanishing (anti-)commutator amongst the creation and annihilation operators of the normal mode expansion of the basic fields of the theory.