Clifford modules and generalized Dirac operators (Q5932510)

The article explains the use of the Dirac operator in theoretical physics. The paper contains a well-written historical overview on the history of the Dirac operator in physics. The author recalls the definition of generalized Dirac operators in the sense of Berline-Getzler-Vergne. Two twisted Dirac operators are of special importance: the Pauli-Dirac operator which arises from coupling with the electrical field, and the Dirac-Yukawa operator that we obtain from coupling with mass. A combination of both operators is used as a term in the action of the Standard Model. The associated Bochner-Weitzenböck formulas are calculated.