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The HMW effect in Noncommutative Quantum Mechanics

Jianhua Wang, Kang Li B

Published Nov 26, 2012• 39 citations
OpenAlex

Abstract

The HMW effect in non-commutative quantum mechanics is studied. By solving the Dirac equations on non-commutative (NC) space and non-commutative phase space, we obtain topological HMW phase on NC space and NC phase space respectively, where the additional terms related to the space-space and momentum-momentum non-commutativity are given explicitly. PACS number(s): 02.40.Gh, 11.10.Nx, 03.65.-w 1

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The HMW effect in non-commutative quantum mechanics is studied. By solving the Dirac equations on non-commutative (NC) space and non-commutative phase space, we obtain topological HMW phase on NC space and NC phase space respectively, where the additional terms related to the space-space and momentum-momentum non-commutativity are given explicitly. PACS number(s): 02.40.Gh, 11.10.Nx, 03.65.-w 1
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In this letter, firstly, the Schrddoto\\ddot{o}ddotodinger equation on noncommutative phase space is given by using a generalized Bopp's shift. Then the anomaly term of commutator of arbitrary physical observable operators on noncommutative phase space is obtained. Finally, the basic uncertainty relations for space-space and space-momentum as well as momentum-momentum operators in noncommutative quantum mechanics (NCQM), and uncertainty relation for arbitrary physical observable operators in NCQM are discussed.