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Title: Noncommutative quantum mechanics as a gauge theory

Abstract

The classical counterpart of noncommutative quantum mechanics is a constrained system containing only second-class constraints. The embedding procedure formulated by Batalin, Fradkin and Tyutin (BFT) enables one to transform this system into an Abelian gauge theory exhibiting only first class constraints. The appropriateness of the BFT embedding, as implemented in this work, is verified by showing that there exists a one to one mapping linking the second-class model with the gauge invariant sector of the gauge theory. As is known, the functional quantization of a gauge theory calls for the elimination of its gauge freedom. Then, we have at our disposal an infinite set of alternative descriptions for noncommutative quantum mechanics, one for each gauge. We study the relevant features of this infinite set of correspondences. The functional quantization of the gauge theory is explicitly performed for two gauges and the results compared with that corresponding to the second-class system. Within the operator framework the gauge theory is quantized by using Dirac's method.

Authors:
;  [1]
  1. Instituto de Fisica, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, 91501-970 - Porto Alegre, RS (Brazil)
Publication Date:
OSTI Identifier:
21301031
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 79; Journal Issue: 12; Other Information: DOI: 10.1103/PhysRevD.79.125024; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMMUTATION RELATIONS; GAUGE INVARIANCE; QUANTIZATION; QUANTUM MECHANICS

Citation Formats

Bemfica, F S, and Girotti, H O. Noncommutative quantum mechanics as a gauge theory. United States: N. p., 2009. Web. doi:10.1103/PHYSREVD.79.125024.
Bemfica, F S, & Girotti, H O. Noncommutative quantum mechanics as a gauge theory. United States. https://doi.org/10.1103/PHYSREVD.79.125024
Bemfica, F S, and Girotti, H O. 2009. "Noncommutative quantum mechanics as a gauge theory". United States. https://doi.org/10.1103/PHYSREVD.79.125024.
@article{osti_21301031,
title = {Noncommutative quantum mechanics as a gauge theory},
author = {Bemfica, F S and Girotti, H O},
abstractNote = {The classical counterpart of noncommutative quantum mechanics is a constrained system containing only second-class constraints. The embedding procedure formulated by Batalin, Fradkin and Tyutin (BFT) enables one to transform this system into an Abelian gauge theory exhibiting only first class constraints. The appropriateness of the BFT embedding, as implemented in this work, is verified by showing that there exists a one to one mapping linking the second-class model with the gauge invariant sector of the gauge theory. As is known, the functional quantization of a gauge theory calls for the elimination of its gauge freedom. Then, we have at our disposal an infinite set of alternative descriptions for noncommutative quantum mechanics, one for each gauge. We study the relevant features of this infinite set of correspondences. The functional quantization of the gauge theory is explicitly performed for two gauges and the results compared with that corresponding to the second-class system. Within the operator framework the gauge theory is quantized by using Dirac's method.},
doi = {10.1103/PHYSREVD.79.125024},
url = {https://www.osti.gov/biblio/21301031}, journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 12,
volume = 79,
place = {United States},
year = {Mon Jun 15 00:00:00 EDT 2009},
month = {Mon Jun 15 00:00:00 EDT 2009}
}