The Cohomology and Homology of Quantum Field Theory
Asked what relativistic quantum field theory contributes to our understanding of physical phenomena, we would point to the anomalous magnetic moment of the electron or the success of the standard model. These are the nuggets of gold from the el dorado of gauge theories. But success and disaster lie close at hand: imagine a gauge theory given in terms of its observable quantites and ask what features might betray its origin as a gauge theory, the suggestions are few and unconvincing. The guiding geometrical ideas, such as Lagrangian, gauge group, gauge—fixing, vector bundles, connexions, curvature, have stolen from the stage. Perhaps gauge theories should have a characteristic structure in non—commutative geometry. Renormalized perturbation theory, designed to deal with divergences, is unlikely to effect a passage from commutative to non—commutative geometry.
KeywordsGauge Theory Minkowski Space Monoidal Category Local Cohomology Weyl Operator
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