Schwinger's picture of quantum mechanics: 2-groupoids and symmetries Articles uri icon

publication date

  • September 2021

start page

  • 333

end page

  • 354

issue

  • 3

volume

  • 13

International Standard Serial Number (ISSN)

  • 1941-4889

Electronic International Standard Serial Number (EISSN)

  • 1941-4897

abstract

  • Starting from the groupoid approach to Schwinger's picture of Quantum Mechanics, a proposal for the description of symmetries in this framework is advanced. It is shown that, given a groupoid associated with a (quantum) system, there are two possible descriptions of its symmetries, one 'microscopic', the other one 'global'. The microscopic point of view leads to the introduction of an additional layer over the grupoid, giving rise to a suitable algebraic structure of 2-groupoid. On the other hand, taking advantage of the notion of group of bisections of a given groupoid, the global perspective allows to construct a group of symmetries out of a 2-groupoid. The latter notion allows to introduce an analog of the Wigner's theorem for quantum symmetries in the groupoid approach to Quantum Mechanics.

subjects

  • Mathematics

keywords

  • bisections; groupoid and group automorphisms; groupoids and 2-groupoids; schwinger┬┐s picture of quantum mechanics; symmetries