Constructive Gauge Theory
Here we provide some insight into mathematical methods to analyze quantized gauge theories. This approach is being used to establish existence as well as to prove properties of gauge field models. Up to now, only abelian gauge fields are known to exist, namely the U(1) Higgs model on ℝ2 and ℝ3 and electrodynamics on the tori T2 and T3. In these lectures we study infrared properties of some of these models. The non-Abelian gauge models are interesting for additional reasons: First, they have a natural geometric interpretation. Furthermore, because of asymptotic freedom, non-Abelian models have better local regularity properties than Abelian theories. Furthermore, they provide a rich analytic structure.
KeywordsGauge Theory Gauge Transformation Gauge Invariance Lattice Gauge Theory Unit Lattice
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