Geometrical description of SU(2) Berry phases

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

The differential geometric background for the occurrence of SU(2) Berry phases in Fermi systems with time-reversal invariance is investigated. We explicitly construct the natural geometric structures on ssHssPn (the quaternionic projective space) responsible for nontrivial holonomy. For the special case n=1, ssHssP1ssS4, the connection that governs the time evolution corresponds to the SU(2) Yang-Mills instanton with self-dual curvature, giving the nonadiabatic generalization of the spin (3/2 case of Avron et al. [Phys. Rev. Lett. 61, 1329 (1988)].

Original languageEnglish
Pages (from-to)2837-2840
Number of pages4
JournalPhysical Review A
Volume41
Issue number5
DOIs
Publication statusPublished - 1990

Fingerprint

instantons
invariance
curvature
occurrences

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Atomic and Molecular Physics, and Optics

Cite this

Geometrical description of SU(2) Berry phases. / Lévay, P.

In: Physical Review A, Vol. 41, No. 5, 1990, p. 2837-2840.

Research output: Contribution to journalArticle

Lévay, P. / Geometrical description of SU(2) Berry phases. In: Physical Review A. 1990 ; Vol. 41, No. 5. pp. 2837-2840.
@article{e2d8953727ff4a079095d2fcbcf69519,
title = "Geometrical description of SU(2) Berry phases",
abstract = "The differential geometric background for the occurrence of SU(2) Berry phases in Fermi systems with time-reversal invariance is investigated. We explicitly construct the natural geometric structures on ssHssPn (the quaternionic projective space) responsible for nontrivial holonomy. For the special case n=1, ssHssP1ssS4, the connection that governs the time evolution corresponds to the SU(2) Yang-Mills instanton with self-dual curvature, giving the nonadiabatic generalization of the spin (3/2 case of Avron et al. [Phys. Rev. Lett. 61, 1329 (1988)].",
author = "P. L{\'e}vay",
year = "1990",
doi = "10.1103/PhysRevA.41.2837",
language = "English",
volume = "41",
pages = "2837--2840",
journal = "Physical Review A",
issn = "2469-9926",
publisher = "American Physical Society",
number = "5",

}

TY - JOUR

T1 - Geometrical description of SU(2) Berry phases

AU - Lévay, P.

PY - 1990

Y1 - 1990

N2 - The differential geometric background for the occurrence of SU(2) Berry phases in Fermi systems with time-reversal invariance is investigated. We explicitly construct the natural geometric structures on ssHssPn (the quaternionic projective space) responsible for nontrivial holonomy. For the special case n=1, ssHssP1ssS4, the connection that governs the time evolution corresponds to the SU(2) Yang-Mills instanton with self-dual curvature, giving the nonadiabatic generalization of the spin (3/2 case of Avron et al. [Phys. Rev. Lett. 61, 1329 (1988)].

AB - The differential geometric background for the occurrence of SU(2) Berry phases in Fermi systems with time-reversal invariance is investigated. We explicitly construct the natural geometric structures on ssHssPn (the quaternionic projective space) responsible for nontrivial holonomy. For the special case n=1, ssHssP1ssS4, the connection that governs the time evolution corresponds to the SU(2) Yang-Mills instanton with self-dual curvature, giving the nonadiabatic generalization of the spin (3/2 case of Avron et al. [Phys. Rev. Lett. 61, 1329 (1988)].

UR - http://www.scopus.com/inward/record.url?scp=4244101546&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4244101546&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.41.2837

DO - 10.1103/PhysRevA.41.2837

M3 - Article

AN - SCOPUS:4244101546

VL - 41

SP - 2837

EP - 2840

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 5

ER -