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Matrix operator symmetries of the Dirac equation and separation of variables

Matrix operator symmetries of the Dirac equation and separation of variables

##### Abstract

The set of all matrix-valued first-order differential operators that commute with the Dirac equation in n-dimensional complex Euclidean space is computed. In four dimensions it is shown that all matrix-valued second-order differential operators that commute with the Dirac operator in four dimensions are obtained as products of first-order operators that commute with the Dirac operator. Finally some additional coordinate systems for which the Dirac equation in Minkowski space can be solved by separation of variables are presented. These new systems are comparable to the separation in oblate spheroidal coordinates discussed by Chandrasekhar [S. Chandrasekhar, The Mathematical Theory of Black Holes (Oxford U.P., Oxford, 1983)].

##### Type

Journal Article

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##### Citation

Kalnins, E.G., Miller, W., Jr. & Williams, G.C. (1986). Matrix operator symmetries of the Dirac equation and separation of variables. Journal of Mathematical Physics, 27, 1893.

##### Date

1986-07

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##### Rights

Copyright 1986 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in the Journal of Mathematical Physics and may be found at http://jmp.aip.org/jmp/top.jsp