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Journal Article

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


Isidro,  Jose M.
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Isidro, J. M. (2008). Quantum mechanics as a spontaneously broken gauge quantum theory o a U(1) gerbe. International Journal of Geometric Methods in Modern Physics, 5(2), 233-252. doi:10.1142/S0219887808002722.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-632E-2
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.