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The Dirac equation in exterior form. (English) Zbl 0587.58002
This paper is a continuation of the authors’ papers [ibid. 89, 341-362 (1983; Zbl 0527.58023); J. Phys. A 16, 4147-4153 (1983); Phys. Lett. B 130, 177-178 (1983)]. The authors, using the correspondence between the Clifford and exterior algebras, have written the Dirac equation in terms of differential forms. The covariances of the theory are examined. The authors have shown in detail the correspondence between an equation for a spinorial section of the Kähler-Atiyah bundle and the usual matrix formulation of the Dirac equation.
Reviewer: J.Kubarsky
MSC:
58A10Differential forms (global analysis)
15A66Clifford algebras, spinors
81Q05Closed and approximate solutions to quantum-mechanical equations
References:
[1]K?hler, E.: Der innere Differentialkalk?l. Rend. Mat. (3-4)21, 425 (1962)
[2]Graf, W.: Differential forms as spinors. Ann. Inst. Henri Poincar?XXIX, 85 (1978)
[3]Benn, I.M., Tucker, R.W.: Fermions without spinors. Commun. Math. Phys.89, 341 (1983) · Zbl 0527.58023 · doi:10.1007/BF01214659
[4]Albert, A.A.: Structure of algebras. American Mathematical Society Colloquium Publications, Vol. XXIV, 1961
[5]Benn, I.M., Tucker, R.W.: Clifford analysis of exterior forms and Fermi-Bose symmetry. J. Phys. A16, 4147 (1983) · doi:10.1088/0305-4470/16/17/029
[6]Lounesto, P.: Scalar products of spinors and an extension of Brauer-Wall groups. Found. Phys.11, 721 (1981) · doi:10.1007/BF00726946
[7]Porteus, I.R.: Topological geometry. Cambridge: Cambridge University Press 1981
[8]Benn, I.M., Tucker, R.W.: A local right-spin covariant K?hler equation. Phys. Lett. B130, 177 (1983) · doi:10.1016/0370-2693(83)91037-7