On the Mickelsson-Faddeev extension and unitary representations

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17 Scopus citations

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 1 1989

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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