Gauge unfixing formalism of the O(N) nonlinear sigma model

Everton Mc Abreu,Jorge A Neto,Albert Cr Mendes

doi:10.15406/oajmtp.2018.01.00007

Abstract

In a few years back, one of us has proposed a new scheme of embedding constrained systems based mainly on the Gauge Unfixing (GU) formalism and it is known as an extended GU formalism. The proposition was to modify directly the original phase space variables of an arbitrary system in order to turn the system a gauge invariant one. Since the new theory is gauge invariant, we can say that the new system is a first class one in Dirac terminology. In this way, the GU method is a constraint conversion technique. In this work, by using this extended GU formalism we have obtained two different versions of the first class system related on the O(N) nonlinear sigma model

Highlights

In this work we will discuss a subject that is still of extreme importance in today’s theoretical physics
The objective was to redefine the original phase space variables of a certain constrained system, without introducing any Wess Zumino (WZ) terms, in order to be gauge invariant fields. Functions of these gauge invariant fields, which will be gauge invariant quantities, were constructed. This so called “extended” Gauge Unfixing (GU) formalism begins with a kind of mixed constrained system, which was the CS theory, at that occasion, and, applying the technique, it was obtained a first−class system which was written just in terms of the original phase space variables with many new features
We have used the so called extended GU formalism which, by gauging the original phase space variables of a constrained system, we can carry out the transformation of a second− class system into a first-class one and thereby, a gauge invariant theory is obtained

Summary

Introduction

In this work we will discuss a subject that is still of extreme importance in today’s theoretical physics. The GU formalism considers part of the whole group of second−class constraints as being the gauge symmetry generators. The corresponding second−class Hamiltonian must be adapted, i.e., modified, in such a convenient way in order to satisfy the first−class algebra together with the constraints that were chosen at the beginning as being the gauge symmetry generators.

Results

Conclusion