Quantum mechanics as a spontaneously broken gauge theory on a U(1) gerbe

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dc.creatorIsidro, J. M.
dc.date2007-08-06
dc.date.accessioned2026-07-07T11:18:26Z
dc.date.available2026-07-07T11:18:26Z
dc.descriptionAny quantum-mechanical system possesses a U(1) gerbe naturally defined on configuration space. Acting on Feynman's kernel exp(iS/h), this U(1) symmetry allows one to arbitrarily pick the origin for the classical action S, on a point-by-point basis on configuration space. This is equivalent to the statement that quantum mechanics is a U(1) gauge theory. Unlike Yang-Mills theories, however, the geometry of this gauge symmetry is not given by a fibre bundle, but rather by a gerbe. Since this gauge symmetry is spontaneously broken, an analogue of the Higgs mechanism must be present. We prove that a Heisenberg-like noncommutativity for the space coordinates is responsible for the breaking. This allows to interpret the noncommutativity of space coordinates as a Higgs mechanism on the quantum-mechanical U(1) gerbe.
dc.identifierhttps://arxiv.org/abs/0708.0720
dc.identifierhttp://arxiv.org/abs/0708.0720
dc.identifierInt.J.Geom.Meth.Mod.Phys.05:233-252,2008
dc.identifierdoi:10.1142/S0219887808002722
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/193343
dc.subjectMathematical Physics
dc.subjectHigh Energy Physics - Theory
dc.subjectQuantum Physics
dc.titleQuantum mechanics as a spontaneously broken gauge theory on a U(1) gerbe
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