Our objective now is to use the machinery assembled in the previous chapter, and that to be developed in subsequent chapters, to study a number of rather specific “classical gauge theories” arising in modern physics. The discussion is heuristic and informal and its intention is to indicate how the topology and geometry that are our real concern here arise naturally in meaningful physics. In order to have a context within which to place these examples we will devote this rather brief section to an explicit enumeration of the basic mathematical ingredients required to describe, at the classical level, the interaction of a particle with a gauge field.
KeywordsDirac Equation Chern Class Matter Field Higgs Field Chern Number
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