Gauge Covariance of the Aharonov-Bohm Phase in Noncommutative Quantum Mechanics

Abstract

The gauge covariance of the wave function phase factor in noncommutative quantum mechanics (NCQM) is discussed. We show that the naive path integral formulation and an approach where one shifts the coordinates of NCQM in the presence of a background vector potential leads to the gauge non-covariance of the phase factor. Due to this fact, the Aharonov-Bohm phase in NCQM which is evaluated through the path-integral or by shifting the coordinates is neither gauge invariant nor gauge covariant. We show that the gauge covariant Aharonov-Bohm effect should be described by using the noncommutative Wilson lines, what is consistent with the noncommutative Schrödinger equation. This approach can ultimately be used for deriving an analogue of the Dirac quantization condition for the magnetic monopole.

18 pages, 1 figure, references added, some points clarified further, minor corrections

References in corpus (3)

• The topological AC effect on noncommutative phase space
• Circumventing the No-Go Theorem in Noncommutative Gauge Field Theory
• A Noncommutative Version of the Minimal Supersymmetric Standard Model

Cited by in corpus (6)

• An Introduction to Noncommutative Physics
• Dirac Quantization Condition for Monopole in Noncommutative Space-Time
• Klein-Gordon theory in noncommutative phase space
• Dynamics of Dipoles and Quantum Phases in Noncommutative Coordinates
• Pinhole interference in three-dimensional fuzzy space
• Chiral Spin Noncommutative Space and Anomalous Dipole Moments