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

Isidro, Jose M.

doi:10.1142/S0219887808002722

アイテム詳細

登録内容を編集ファイル形式で保存

一時保存へ追加

タグ情報を表示リリース履歴を表示詳細要約

公開

学術論文

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

There are no locators available

Fulltext (restricted access)

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

フルテキスト (公開)

公開されているフルテキストはありません

付随資料 (公開)

There is no public supplementary material available

引用

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.

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

要旨

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.