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

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