Symmetry Operators and Separation of Variables for Dirac's Equation on Two-Dimensional Spin Manifolds
Mathematical Physics
2011-06-16 v2 math.MP
Exactly Solvable and Integrable Systems
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.
Keywords
Cite
@article{arxiv.1102.0065,
title = {Symmetry Operators and Separation of Variables for Dirac's Equation on Two-Dimensional Spin Manifolds},
author = {Alberto Carignano and Lorenzo Fatibene and Raymond G. McLenaghan and Giovanni Rastelli},
journal= {arXiv preprint arXiv:1102.0065},
year = {2011}
}
Comments
This paper is dedicated to Professor Willard Miller, Jr. on the occasion of his retirement from the School of Mathematics at the University of Minnesota