Quantum mechanics as a spontaneously broken gauge theory on a U(1) gerbe
Abstract
Any 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.
Keywords
Cite
@article{arxiv.0708.0720,
title = {Quantum mechanics as a spontaneously broken gauge theory on a U(1) gerbe},
author = {J. M. Isidro},
journal= {arXiv preprint arXiv:0708.0720},
year = {2008}
}