Absolute anticommutativity of the nilpotent symmetries in the Hamiltonian formalism: free Abelian 2-form gauge theory

TL;DR

This paper demonstrates that Curci-Ferrari type restrictions in a 4D free Abelian 2-form gauge theory are invariant under time evolution, ensuring the absolute anticommutativity of off-shell nilpotent (anti-) BRST and (anti-) co-BRST symmetries.

Contribution

It establishes the time-evolution invariance of CF-type restrictions, providing a logical basis for their role in ensuring symmetry anticommutativity in Hamiltonian formalism.

Findings

CF restrictions are secondary constraints that remain invariant over time.

Time-evolution invariance ensures independence of symmetry transformations.

Provides a Hamiltonian perspective on symmetry properties.

Abstract

The celebrated Curci-Ferrari (CF) type of restrictions are invoked to obtain the off-shell nilpotent and absolutely anticommuting (anti-) BRST as well as (anti-) co-BRST symmetry transformations in the context of the Lagrangian description of the physical four (3 + 1)-dimensional (4D) free Abelian 2-form gauge theory. We show that the above CF type conditions, which turn out to be the secondary constraints of the theory, remain invariant with respect to the time-evolution of the above 2-form gauge system in the Hamiltonian formulation. This time-evolution invariance (i) physically ensures the linear independence of the BRST versus anti-BRST as well as co-BRST versus anti-co-BRST symmetry transformations, and (ii) provides a logical reason behind the imposition of the above CF type restrictions in the proof of the absolute anticommutativity of the off-shell nilpotent (anti-) BRST as well as (anti-) co-BRST symmetry transformations.