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

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Author(s): Alberto Carignano | Lorenzo Fatibene | Raymond G. McLenaghan | Giovanni Rastelli

Journal: Symmetry, Integrability and Geometry : Methods and Applications
ISSN 1815-0659

Volume: 7;
Start page: 057;
Date: 2011;
Original page

Keywords: Dirac equation | symmetry operators | separation of variables

ABSTRACT
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.
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