arXiv:0708.0720 · International Journal of Geometric Methods in Modern Physics

QUANTUM MECHANICS AS A SPONTANEOUSLY BROKEN GAUGE THEORY ON A U(1) GERBE

J. M. Isidro

Published Mar 1, 2008• 5 citations

Abstract

Any quantum-mechanical system possesses a U(1) gerbe naturally defined on configuration space. Acting on Feynman's kernel exp(iS/ħ), 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.

DOI: 10.1142/s0219887808002722

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