Invariância de calibre e análise de vínculos em teorias de campo eletromagnético no espaço-tempo não-comutativo

Abstract

In this work we will analyse the contributions of non-commutative (NC) to the Proca electrodynamics and also Podolsky's electrodynamics. The NC Proca model is originally not gauge invariant. Here we find, through the gauge unfixing method, a gauge invariant Hamiltonian. With respect to the Podolsky model, we used de Moyal product and the Seiberg-Witten map to analyze the NC contributions to this model. The first important aspect is the gauge invariance. The Podolky model is originally gauge invariant, however, in NC space the Lagrangian in not gauge invariant through the same transformations. Using the Noether method, we find a dual action gauge invariant and we calculate the symmetries. Then, we make the quantization for the NC Podolsky model through two formalism: the Dirac and the Faddev-Jackiw. A comparison is make between this two methods.