Matrix operator symmetries of the Dirac equation and separation of variables

E. G. Kalnins, W. Miller, G. C. Williams

Research output: Contribution to journalArticlepeer-review

32 Scopus citations

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)].

Original languageEnglish (US)
Pages (from-to)1893-1900
Number of pages8
JournalJournal of Mathematical Physics
Volume27
Issue number7
DOIs
StatePublished - 1986

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