The canonical connection in quantum mechanics

Péter Lévay, David McMullan, Izumi Tsutsui

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

In this paper we investigate the form of induced gauge fields that arises in two types of quantum systems. In the first we consider quantum mechanics on coset spaces G/H, and argue that G invariance is central to the emergence of the H connection as induced gauge fields in the different quantum sectors. We then demonstrate why the same connection, now giving rise to the non-Abelian generalization of Berry's phase, can also be found in systems that have slow variables taking values in such a coset space.

Original languageEnglish
Pages (from-to)625-636
Number of pages12
JournalJournal of Mathematical Physics
Volume37
Issue number2
DOIs
Publication statusPublished - Feb 1996

Fingerprint

Coset
Gauge Field
Quantum Mechanics
quantum mechanics
Berry Phase
G-space
Quantum Systems
invariance
Invariance
Sector
sectors
Demonstrate
Generalization
Form

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

The canonical connection in quantum mechanics. / Lévay, Péter; McMullan, David; Tsutsui, Izumi.

In: Journal of Mathematical Physics, Vol. 37, No. 2, 02.1996, p. 625-636.

Research output: Contribution to journalArticle

Lévay, Péter ; McMullan, David ; Tsutsui, Izumi. / The canonical connection in quantum mechanics. In: Journal of Mathematical Physics. 1996 ; Vol. 37, No. 2. pp. 625-636.
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