BRST Invariant Theory Of A Generalized 1+1 Dimensional Nonlinear Sigma Model With Topological Term

TL;DR

This paper develops a BRST invariant formulation of a generalized 1+1 dimensional O(3) nonlinear sigma model with topological terms, addressing constraints and gauge symmetries to deepen understanding of its quantum structure.

Contribution

It introduces a generalized Lagrangian with subsidiary constraints, derives the gauge generator, and explores BRST transformations and ghost field relations in the model.

Findings

Identified a lost intrinsic constraint condition.

Derived the gauge generator and BRST transformations.

Established the general commutation relations of ghost fields.

Abstract

We give a generalized Lagrangian density of 1+1 Dimensional O(3) nonlinear sigma model with subsidiary constraints, different Lagrange multiplier fields and topological term, find a lost intrinsic constraint condition, convert the subsidiary constraints into inner constraints in the nonlinear sigma model, give the example of not introducing the lost constraint, by comparing the example with the case of introducing the lost constraint, we obtain that when not introducing the lost constraint, one has to obtain a lot of various non-intrinsic constraints. We further deduce the gauge generator, give general BRST transformation of the model under the general conditions. It is discovered that there exists a gauge parameter originating from the freedom degree of BRST transformation in a general O(3) nonlinear sigma model, and we gain the general commutation relations of ghost field.