Curci-Ferrari Type Condition in Hamiltonian Formalism: A Free Spinning Relativistic Particle

TL;DR

This paper explores the CF-type restriction in a free spinning relativistic particle, demonstrating its time-evolution invariance and its role in ensuring the independence of BRST and anti-BRST symmetries within Hamiltonian formalism.

Contribution

It establishes the CF-condition as a secondary, time-invariant constraint in Hamiltonian formalism, linking it to BRST symmetry properties in a spinning particle model.

Findings

CF-condition is a secondary constraint.

CF-condition remains invariant under time evolution.

It confirms the independence of BRST and anti-BRST symmetries.

Abstract

The Curci-Ferrari (CF)-type of restriction emerges in the description of a free spinning relativistic particle within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism when the off-shell nilpotent and absolutely anticommuting (anti-)BRST symmetry transformations for this system are derived from the application of horizontality condition (HC) and its supersymmetric generalization (SUSY-HC) within the framework of superfield formalism. We show that the above CF-condition, which turns out to be the secondary constraint of our present theory, remains time-evolution invariant within the framework of Hamiltonian formalism. This time-evolution invariance (i) physically justifies the imposition of the (anti-)BRST invariant CF-type condition on this system, and (ii) mathematically implies the linear independence of BRST and anti-BRST symmetries of our present theory.