Physics – Quantum Physics
Scientific paper
1999-08-04
Int.J.Mod.Phys. A15 (2000) 4903-4932
Physics
Quantum Physics
22 pages, no figures, plain LaTeX file; changes only in details of affiliation and financial support
Scientific paper
10.1142/S0217751X00002844
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.
Govaerts Jan
Villanueva Victor M.
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