On the Mickelsson-Faddeev extension and unitary representations

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

The Mickelsson-Faddeev extension is a 3-space analogue of a Kac-Moody group, where the central charge is replaced by a space of functions of the gauge potential. This extension is a pullback of a universal extension, where the gauge potentials are replaced by operators in a Schatten ideal, as in non-commutative differential geometry. Our main result is that the universal extension cannot be faithfully represented by unitary operators on a separable Hilbert space. We also examine potential consequences of the existence of unitary representations for the Mickelsson-Faddeev extension.

Original languageEnglish (US)
Pages (from-to)617-625
Number of pages9
JournalCommunications in Mathematical Physics
Volume123
Issue number4
DOIs
StatePublished - Dec 1989

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Unitary Representation
Gauge
Kac-Moody Group
differential geometry
operators
Noncommutative Geometry
Unitary Operator
Separable Hilbert Space
Pullback
Differential Geometry
Hilbert space
Charge
analogs
Analogue
Operator

ASJC Scopus subject areas

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

Cite this

On the Mickelsson-Faddeev extension and unitary representations. / Pickrell, Douglas M.

In: Communications in Mathematical Physics, Vol. 123, No. 4, 12.1989, p. 617-625.

Research output: Contribution to journalArticle

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