Open AccessMatrix operator symmetries of the Dirac equation and separation of variables
Author(s) -
E. G. Kalnins,
Willard Miller,
Gareth Williams
Publication year - 1986
Publication title -
journal of mathematical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.708
H-Index - 119
eISSN - 1089-7658
pISSN - 0022-2488
DOI - 10.1063/1.527395
Subject(s) - dirac equation , dirac algebra , dirac operator , clifford analysis , minkowski space , separation of variables , mathematics , dirac spinor , two body dirac equations , chandrasekhar limit , causal fermion system , mathematical physics , mathematical analysis , matrix (chemical analysis) , differential equation , differential operator , dirac (video compression format) , operator (biology) , euclidean space , dirac sea , partial differential equation , physics , quantum mechanics , dirac fermion , stars , materials science , fermion , composite material , astronomy , neutrino , white dwarf , repressor , chemistry , biochemistry , transcription factor , gene
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)]
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