Holonomy Quantization of Moduli Spaces & Grothendieck Groups

TL;DR

This paper explores the holonomy quantization of monopole moduli spaces using graph-based methods to construct C* algebras, linking topological and algebraic structures in mathematical physics.

Contribution

It introduces a novel approach to quantize moduli spaces via holonomy and graph methods, connecting them to C* algebras and Grothendieck groups.

Findings

Constructed C* algebra from monopole moduli space loops

Established a conjectured map between algebra projectors and moduli space

Demonstrated the applicability of holonomy quantization in this context

Abstract

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.