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28 March 2024
 
  » arxiv » quant-ph/9908014

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Topology Classes of Flat U(1) Bundles and Diffeomorphic Covariant Representations of the Heisenberg Algebra
Jan Govaerts ; Victor M. Villanueva ;
Date 4 Aug 1999
Journal Int.J.Mod.Phys. A15 (2000) 4903-4932
Subject Quantum Physics; Mathematical Physics | quant-ph hep-th math-ph math.MP
AffiliationCatholic Univ. Louvain) and Victor M. Villanueva (Univ. Michoacan, Mexico
AbstractThe general construction of self-adjoint configuration space representations of the Heisenberg algebra over an arbitrary manifold is considered. All such inequivalent representations are parametrised in terms of the topology classes of flat U(1) bundles over the configuration space manifold. In the case of Riemannian manifolds, these representations are also manifestly diffeomorphic covariant. The general discussion, illustrated by some simple examples in non relativistic quantum mechanics, is of particular relevance to systems whose configuration space is parametrised by curvilinear coordinates or is not simply connected, which thus include for instance the modular spaces of theories of non abelian gauge fields and gravity.
Source arXiv, quant-ph/9908014
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