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

Isidro, Jose M.

doi:10.1142/S0219887808002722

Item

ITEM ACTIONSEXPORT

Add to Basket

Local TagsRelease HistoryDetailsSummary

Released

Journal Article

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

MPS-Authors

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

External Resource

No external resources are shared

Fulltext (restricted access)

There are currently no full texts shared for your IP range.

Fulltext (public)

There are no public fulltexts stored in PuRe

Supplementary Material (public)

There is no public supplementary material available

Citation

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

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.