Noncommutative quantum mechanics: Uniqueness of the functional description

F. S. Bemfica and H. O. Girotti
Phys. Rev. D 78, 125009 – Published 8 December 2008

Abstract

The generalized Weyl transform of index α is used to implement the time-slice definition of the phase space path integral yielding the Feynman kernel in the case of noncommutative quantum mechanics. As expected, this representation for the Feynman kernel is not unique but labeled by the real parameter α. We succeed in proving that the α-dependent contributions disappear at the limit where the time slice goes to zero. This proof of consistency turns out to be intricate because the Hamiltonian involves products of noncommuting operators originating from the noncommutativity. The antisymmetry of the matrix parametrizing the noncommutativity plays a key role in the cancellation mechanism of the α-dependent terms.

  • Received 7 October 2008

DOI:https://doi.org/10.1103/PhysRevD.78.125009

©2008 American Physical Society

Authors & Affiliations

F. S. Bemfica* and H. O. Girotti

  • Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, 91501-970–Porto Alegre, RS, Brazil

  • *fbemfica@if.ufrgs.br
  • hgirotti@if.ufrgs.br

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Issue

Vol. 78, Iss. 12 — 15 December 2008

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