Simetria de Calibre do modelo de Schwinger Quiral via o formalismo gauge unfixing aprimorado

Abstract

In this work, it is explored the Hamiltonian structure of the Chiral Schwinger model in its bozonized form. From the consistency condition of the constraints, applied in the Dirac method, one knows that this model naturally presents, for certain values of a parameter α, two second class constraints, which means that this system does not possess gauge invariance. However, one knows that is possible to disclose gauge symmetries in such a system, by converting the original second class system into a first class one (possessing gauge invariance). This procedure can be done through the Gauge Unfixing method, by acting with a projection operator directly on the original second class Hamiltonian, without adding extra degrees of freedom in the phase space. One of the constraints is disregarded, and the other one becomes the gauge symmetry generator of the theory. At the end, the result is a first class Hamiltonian satisfying a first class algebra. But, there is an improved version of this method, in which the phase space variables are redefined in order to construct first class functions of these variables. The goal of this work is to apply the improved gauge unfixing formalism to the Chiral Schwinger model to disclose the hidden gauge symmetries of the system. Two gauge invariant theories are obtained, in which the Poisson Brackets between the new functions are consistent with the Dirac brackets involving the original ones.