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

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

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...

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Bibliographic Details
Main Authors: Alberto Carignano, Lorenzo Fatibene, Raymond G. McLenaghan, Giovanni Rastelli
Format: Article
Language:English
Published: National Academy of Science of Ukraine 2011-06-01
Series:Symmetry, Integrability and Geometry: Methods and Applications
Subjects:
Dirac equation
symmetry operators
separation of variables
Online Access:http://dx.doi.org/10.3842/SIGMA.2011.057
Description
Summary: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.
ISSN:1815-0659

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