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Symmetry Operators and Separation of Variables for Dirac's Equation on Two-Dimensional Spin Manifolds
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7
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Symmetry Operators and Separation of Variables for Dirac's Equation on Two-Dimensional Spin Manifolds
Інший ID:
2010 Mathematics Subject Classification: 70S10; 81Q80
DOI:10.3842/SIGMA.2011.057
DOI:10.3842/SIGMA.2011.057
Посилання:
Symmetry Operators and Separation of Variables for Dirac's Equation on Two-Dimensional Spin Manifolds / A. Carignano , L. Fatibene, R.G. McLenaghan, G. Rastelli // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 25 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue “Symmetry, Separation, Super-integrability and Special Functions (S⁴)”. The full collection is available at http://www.emis.de/journals/SIGMA/S4.html.
The authors wish to thank their reciprocal institutions, the Dipartimento di Matematica, Universit`a di Torino and the Department of Applied Mathematics, University of Waterloo for hospitality during which parts of this paper were written. The research was supported in part by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada.
Дата:
2011
Переглядів:
450
Завантажень:
245
Анотація:
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.
