Modified gauge unfixing formalism and gauge symmetries in the non-commutative chiral bosons theory

TL;DR

This paper applies a modified gauge unfixing formalism to a noncommutative chiral bosons model, revealing hidden gauge symmetries and constructing gauge-invariant formulations without adding extra degrees of freedom.

Contribution

It introduces a modified gauge unfixing approach directly to second-class variables in a noncommutative chiral bosons model, uncovering new gauge symmetries and formulating gauge-invariant Hamiltonians.

Findings

Two gauge-invariant versions of the NCCB system were constructed.

Deformed Dirac brackets were computed for the noncommutative phase space.

A consistent phase space partition function for quantization was derived.

Abstract

We use the gauge unfixing (GU) formalism framework in a two dimensional noncommutative chiral bosons (NCCB) model to disclose new hidden symmetries. That amounts to converting a second-class system to a first-class one without adding any extra degrees of freedom in phase space. The NCCB model has two second-class constraints -- one of them turns out as a gauge symmetry generator while the other one, considered as a gauge-fixing condition, is disregarded in the converted gauge-invariant system. We show that it is possible to apply a conversion technique based on the GU formalism direct to the second-class variables present in the NCCB model, constructing deformed gauge-invariant GU variables, a procedure which we name here as modified GU formalism. For the canonical analysis in noncommutative phase space, we compute the deformed Dirac brackets between all original phase space variables. We obtain two different gauge invariant versions for the NCCB system and, in each case, a GU Hamiltonian is derived satisfying a corresponding first-class algebra. Finally, the phase space partition function is presented for each case allowing for a consistent functional quantization for the obtained gauge-invariant NCCB.