On the Problem of the Amenability of the Gauge Group |
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Authors: | Carey Alan Grundling Hendrik |
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Affiliation: | (1) Mathematical Sciences Institute, Bldg 27, Australian National University, ACT 0200, Australia;(2) Department of Mathematics, University of New South Wales, Sydney, NSW 2052, Australia |
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Abstract: | Let G be one of the local gauge groups C(X, U(n)),C(X, U(n)), C(X, SU(n)) or C(X, SU(n)) where X is a compact Riemannian manifold. We observe that G has a nontrivial group topology, coarser than its natural topology, w.r.t. which it is amenable, viz. the relative weak topology of C(X, M(n)). This topology seems more useful than other known amenable topologies for G. We construct a simple fermionic model containing an action of G, continuous w.r.t. this amenable topology. |
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Keywords: | gauge group amenability mean invariant vacuum quantised gauge theory |
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