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The Clifford algebra of differential forms

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Abstract

This paper reviews Clifford algebras in mathematics and in theoretical physics. In particular, the little-known differential form realization is constructed in detail for the four-dimensional Minkowski space. This setting is then used to describe spinors as differential forms, and to solve the Klein-Gordon and Kähler-Dirac equations. The approach of this paper, in obtaining the solutions directly in terms of differential forms, is much more elegant and concise than the traditional explicit matrix methods. A theorem given here differentiates between the two real forms of the Dirac algebra by showing that spin can be accommodated in only one of them.

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  1. Division of Mathematics, Computer Science, and Systems Design, The University of Texas at San Antonio, 78285, San Antonio, TX, U.S.A.

    N. A. Salingaros & G. P. Wene

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Salingaros, N.A., Wene, G.P. The Clifford algebra of differential forms. Acta Appl Math 4, 271–292 (1985). https://doi.org/10.1007/BF00052466

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