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.

Accepted for publication in Physical Review D

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Cited by in corpus (7)

• A comparative review of four formulations of noncommutative quantum mechanics
• Noncommutativity due to spin
• Dynamical noncommutativity
• Twist Deformation of Rotationally Invariant Quantum Mechanics
• Canonical Structure of Noncommutative Quantum Mechanics as Constraint System
• From Noncommutative Sphere to Nonrelativistic Spin
• Alternative Approach to Noncommutative Quantum Mechanics on a Curved Space