The classification of complete sets of operators commuting with the Dirac operator in Minkowski space-time

DOI10.1063/1.528028zbMath0644.58039OpenAlexW2035420657MaRDI QIDQ3787183

Niky Kamran, Robert S. Winternitz, Martin Legare, Raymond G. Mclenaghan

Publication date: 1988

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.528028

zbMATH Keywords

Dirac operatorPoincaré groupself-adjoint first-order matrix differential operators

Mathematics Subject Classification ID

Quantum field theory on curved space or space-time backgrounds (81T20) Applications of global analysis to the sciences (58Z05) Infinite-dimensional Lie (super)algebras (17B65) Methods of quantum field theory in general relativity and gravitational theory (83C47) Applications of PDEs on manifolds (58J90)

Cites Work

• Killing tensors and the separation of the Hamilton-Jacobi equation
• Separable systems of Stäckel
• Conformal Killing Tensors and Variable Separation for Hamilton–Jacobi Equations
• On separable solutions of Dirac’s equation for the electron
• Subgroups of the Poincaré group and their invariants
• Separation of variables and symmetry operators for the neutrino and Dirac equations in the space-times admitting a two-parameter abelian orthogonally transitive isometry group and a pair of shearfree geodesic null congruences
• Matrix operator symmetries of the Dirac equation and separation of variables

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