Definition of Magnetic Monopole Numbers for SU(N) Lattice Gauge-Higgs Models
S. Hollands (U. of York), M. Mueller-Preussker (Humboldt-U.)
TL;DR
This paper introduces a gauge-invariant, topologically stable geometric definition of magnetic monopole numbers in SU(N) lattice gauge-Higgs models, generalizing previous SU(2) methods.
Contribution
It provides a new geometric and topological framework for defining magnetic monopole charges in SU(N) lattice gauge theories with Higgs fields, without gauge fixing.
Findings
The local monopole number is gauge-invariant and stable.
The method generalizes previous SU(2) monopole definitions.
A detailed calculation prescription is provided.
Abstract
A geometric definition for a magnetic charge of Abelian monopoles in SU(N) lattice gauge theories with Higgs fields is presented. The corresponding local monopole number defined for almost all field configurations does not require gauge fixing and is stable against small perturbations. Its topological content is that of a 3-cochain. A detailed prescription for calculating the local monopole number is worked out. Our method generalizes a magnetic charge definition previously invented by Phillips and Stone for SU(2).
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