ON THE LOCAL STRUCTURE OF THE REPRESENTATION OF A LOCAL GAUGE GROUP
Copyright policy )ON THE LOCAL STRUCTURE OF THE REPRESENTATION OF A LOCAL GAUGE GROUP
We discuss the local structure of the net [Formula: see text] of von Neumann algebras generated by a representation of a local gauge group [Formula: see text]. Our discussion is independent of the singularity of spectral measures, which has been discussed by many authors since the pioneering work of Gelfand–Graev–Veršic. We show that, for type (S) operators UA,b, second quantized operators with some twists, the commutativity only with those U(ψ) is sufficient for the triviality of them, where ψ belongs to an arbitrary (small) neighborhood of constant function 1. Some properties of 1-cocycles for the representation V : ψ ↦ Adψare also discussed.
type (S) representation, Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations, Infinite-dimensional Lie groups and their Lie algebras: general properties, FOS: Physical sciences, Mathematical Physics (math-ph), 06B15; 06B05, Energy representation, Representation theory of lattices, Fock space, gauge group, energy representation, 06B05, Applications of Lie groups to the sciences; explicit representations, 06B15, Mathematical Physics
type (S) representation, Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations, Infinite-dimensional Lie groups and their Lie algebras: general properties, FOS: Physical sciences, Mathematical Physics (math-ph), 06B15; 06B05, Energy representation, Representation theory of lattices, Fock space, gauge group, energy representation, 06B05, Applications of Lie groups to the sciences; explicit representations, 06B15, Mathematical Physics
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