On Irreducibility of the Energy Representation of the Gauge Group and the White Noise Distribution Theory
نویسنده
چکیده
We consider the energy representation for the gauge group. The gauge group is the set of C∞mappings from a compact Riemannian manifold to a semi-simple compact Lie group. In this paper, we obtain irreducibility of the energy representation of the gauge group for any dimension of M . To prove irreducibility for the energy representation, we use the fact that each operator from a space of test functionals to a space of generalized functionals is realized as a series of integral kernel operators, called the Fock expansion.
منابع مشابه
White Noise Analysis on manifolds and irreducibility of the energy representation of a gauge group
The energy representation of a gauge group on a Riemannian manifold has been discussed by several authors, for instance, in Refs. 1, 2, 4, 5, 7 and 13. Their methods are essentially to reduce the problem to the estimate of the support of a Gaussian measure in an infinite dimensional space. The best result in this direction seems to be the one in Ref. 13. After all these contributions, the irred...
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