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Dirac and Maxwell equations in the Clifford and spin-Clifford bundles. (English) Zbl 0699.53020
The present paper is a direct continuation of a previous one by V. L. Figueiredo and the authors [ibid., 371-395 (1990; see the preceding review)] in which the Dirac and Maxwell equations are investigated in some detail. These equations are considered in generalized form (including the possibility of monopoles) and it is shown that all known presentations of the Maxwell equations in (matrix) Dirac-like “spinor” form can be obtained by choosing particular global idempotents in the indicated Clifford bundles. They also consider the transformation laws of these equations under the Lorentz group and resolve several misunderstandings which have previously appeared in the literature. Finally a factorization of the Maxwell field into two-component spinor fields is exhibited.
Reviewer: J.D.Zund

MSC:
53C27 Spin and Spin\({}^c\) geometry
83C60 Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism
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