Topology classes of flat U(1) bundles and diffeomorphic covariant representations of the Heisenberg algebra

Govaerts, Jan;Villanueva, Victor M.
(2000) International Journal of Modern Physics A : particles and fields; gravitation; cosmology; nuclear physics — Vol. A15, p. 4903-4932 (2000)

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  • Govaerts, Janorcid-logoUCLouvain
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  • Villanueva, Victor M.
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Abstract
(en) The 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. Comment: 22 pages, no figures, plain LaTeX file; changes only in details of affiliation and financial support
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Govaerts, J., & Villanueva, V. M. (2000). Topology classes of flat U(1) bundles and diffeomorphic covariant representations of the Heisenberg algebra. International Journal of Modern Physics A : Particles and Fields; Gravitation; Cosmology; Nuclear Physics, A15, 4903-4932. https://hdl.handle.net/2078.5/257099 (Original work published 2000)