Symmetry Operators and Separation of Variables for Dirac's Equation on Two-Dimensional Spin Manifolds

Alberto Carignano ; Lorenzo Fatibene ; Raymond G. McLenaghan ; Giovanni Rastelli

Symmetry, integrability and geometry: methods and applications, Tome 7 (2011)

Résumé

A signature independent formalism is created and utilized to determine the general second-order symmetry operators for Dirac's equation on two-dimensional Lorentzian spin manifolds. The formalism is used to characterize the orthonormal frames and metrics that permit the solution of Dirac's equation by separation of variables in the case where a second-order symmetry operator underlies the separation. Separation of variables in complex variables on two-dimensional Minkowski space is also considered.

Détail

Keywords: Dirac equation; symmetry operators; separation of variables.

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