Holonomy Quantization of Moduli Spaces & Grothendieck Groups

Details Holonomy Quantization of Moduli Spaces & Grothendieck Groups Holonomy Quantization of Moduli Spaces & Grothendieck Groups

2004-09-01

arxiv.org/abs/hep-th/0409016v1

Physics

High Energy Physics

High Energy Physics - Theory

21 pages

Scientific paper

Gelfand's charecterization of a topological space M by the duality relationship of M and $\mathcal{A} = \mathcal{F}(M)$, the commutative algebra of functions on this space has deep implications including the development of spectral calculas by Connes .We investigate this scheme in this paper in the context of Monopole Moduli Space $\mathcal{M}$ using Seiberg-Witten Equations. A observation has been made here that the methods of holonomy quantization using graphs can be construed to construct a C* algebra corresponding to the loop space of the Moduli. A map is thereby conjectured with the corresponding projectors of the algebra with the moduli space.

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