Holonomy and Skyrme's Model

Dave Auckly, Lev Kapitanski

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

In this paper we consider two generalizations of the Skyrme model. One is a variational problem for maps from a compact 3-manifold to a compact Lie group. The other is a variational problem for flat connections. We describe the path components of the configuration spaces of smooth fields for each of the variational problems. We prove that the invariants separating the path components are well-defined for (not necessarily smooth) fields with finite Skyrme energy. We prove that for every possible value of these invariants there exists a minimizer of the Skyrme functional. Throughout the paper we emphasize the importance of holonomy in the Skyrme model. Some of the results may be useful in other contexts. In particular, we define the holonomy of a distributionally flat Lloc 2 connection; the local developing maps for such connections need not be continuous.

Original languageEnglish (US)
Pages (from-to)97-122
Number of pages26
JournalCommunications in Mathematical Physics
Volume240
Issue number1-2
DOIs
StatePublished - Sep 2003
Externally publishedYes

Fingerprint

Holonomy
Variational Problem
Flat Connection
Path
Invariant
Compact Lie Group
Minimizer
Configuration Space
Well-defined
configurations
Model
Energy
energy

ASJC Scopus subject areas

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

Cite this

Holonomy and Skyrme's Model. / Auckly, Dave; Kapitanski, Lev.

In: Communications in Mathematical Physics, Vol. 240, No. 1-2, 09.2003, p. 97-122.

Research output: Contribution to journalArticle

Auckly, Dave ; Kapitanski, Lev. / Holonomy and Skyrme's Model. In: Communications in Mathematical Physics. 2003 ; Vol. 240, No. 1-2. pp. 97-122.
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