2010/01/13 by Éverton M. C. Abreu, E. M. C. Abreu, Abreu, E. M. C. +8
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #Numerical methods for differential equations #hep-th
paper · pdf · doi:10.48550/arxiv.1001.2254
24 pages. Revtex 4.1. Subtractions were made
openalex publication_date 2010/01/13 · arxiv created 2010/01/19 · arxiv updated 2010/02/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The concept of gauge invariance can be considered one of the most subtle and useful concept in theoretical physics since it can permit the comprehension of difficult systems in physics with an arbitrary choice of a reference frame at every instant of time. It is always desirable to have a bridge between gauge invariant and noninvariant theories. Once established, this kind of mapping between first-class (gauge invariant) and second-class systems, in Dirac's formalism can be considered as a sort of duality. In this paper we investigate this "duality" obtaining a gauge invariant theory starting with a noninvariant one. We analyzed both Abelian and non-Abelian theories and the procedure used is the recent dual (also called symplectic) embedding formalism. We believe that this method is the most convenient one since it is not plagued by the ambiguity problems that torments BFFT and other iterative methods. We demonstrated exactly that this "dualization" method used here does not require any special modification to handle with non-Abelian systems, which is also a new result described in this paper. To prove the gauge invariance we used just the Dirac constraint technique. It is relevant to say here that, although this work is lengthy, the majority of the results presented here are new in the literature. The results that are not new were reproduced within a new perspective.