In Part II, we expounded Shale-Stinespring theory and exhibited the abstract charged field as the simplest example of a summable Fredholm module, and thus a source of noncommutative geometry. Having come so far, it would be a pity not to develop fermion quantum dynamics in external fields, which comes straight from the spin representation. As on many occasions in this book, we set to work here on an enterprise of translation; in this case, to render in algebraic terms the quantization of wave equations of the Dirac type. Most of the footwork has already been laid in Section 6.4.
KeywordsQuantum Theory Dirac Equation Hopf Algebra Dirac Operator Spin Representation
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