Quaternionic gauge fields and the geometric phase

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

The quaternionic representation of the SU(2) non-Abelian, nonadiabatic geometric phase for Fermi systems with time reversal invariance is investigated. The underlying differential geometric structure originating from the Riemannian metric on HPn (the quaternionic projective space) is studied in detail. For two simple model Hamiltonians corresponding to the cases of adiabatic, and nonadiabatic cyclic evolutions, the gauge fields are shown to be identical with Yang's SU(2) monopole solutions. This example of nonadiabatic cyclic evolution turns out to be useful in the context of Polyakov's spin factors also. Employing bosonic degrees of freedom interacting with the fermionic ones, it is found that the gauge structures are also present in the bosonic effective action. However, this topological part of the effective action cannot solely be interpreted as a Wess-Zumino term unlike the one in the complex case.

Original languageEnglish
Pages (from-to)2347-2357
Number of pages11
JournalJournal of Mathematical Physics
Volume32
Issue number9
Publication statusPublished - 1991

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Geometric Phase
Effective Action
Gauge Field
Gages
Hamiltonians
Time Reversal
Monopole
Geometric Structure
Riemannian Metric
Invariance
Projective Space
monopoles
invariance
Gauge
degrees of freedom
Degree of freedom
Term
Model
Context

ASJC Scopus subject areas

  • Organic Chemistry

Cite this

Quaternionic gauge fields and the geometric phase. / Lévay, P.

In: Journal of Mathematical Physics, Vol. 32, No. 9, 1991, p. 2347-2357.

Research output: Contribution to journalArticle

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