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  • American Institute of Physics (AIP)  (3)
  • 1
    Electronic Resource
    Electronic Resource
    Dirac equation in external fields: Separation of variables in nondiagonal metrics (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 297-303 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The algebraic method of separation of variables in the Dirac equation proposed in earlier works by one of the present authors [Theor. Math. Phys. 70, 204 (1987); J. Math. Phys. 30, 2132 (1989)] is developed for the space-time with nondiagonal metrics. The essence of the method consists of the separation of the first-order matricial differential operators that define the dependence of the Dirac's bispinor on the related variables. In contrast to some other authors the pairs of operators are commuted on each step of separation including the variables mixed by nondiagonal elements of fundamental tensor of space-time. There are reasons to believe that it must be some local similarity transformation connected these commuted operators with noncommuted corresponding operators of other authors, although such transformation in view of mathematical difficulties of problem, in general, were not successfully found.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529964
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Dirac equation in external fields: Separation of variables in curvilinear coordinates (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 914-925 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The algebraic method of separation of variables in the Dirac equation proposed by one of the present authors [Gravitation and Electromagnetism (U.P., Minsk, 1989) Issue 4, p. 156 (in Russian)] is developed for the case of the most general interaction of the Dirac particle in an external field, taking into account scalar, vector, tensor, pseudovector, pseudoscalar, and gravitation connections. The present work, which concludes this series of papers entitled "Dirac equation in external fields'' [J. Math. Phys. 32, 3184 (1991); 33, XXX (1992)] is dedicated to the investigation of the problem in the case of general orthogonal curvilinear coordinates, and allows the introduction of gravitation through the spinor connection and Lame's functions. Special consideration is given to the cases, when the generalized Lame's functions do not separate the variables multiplicatively (e.g., elliptic cylindrical, parabolic cylindrical, and oblate and prolate spheroidal coordinates). All the previous results and numerous results of other authors are particular cases of this investigation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529743
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    The Dirac equation in external fields: Variable separation in Cartesian coordinates (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 3184-3188 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The method of separation of variables in the Dirac equation proposed in an earlier work by one of the present authors [J. Math. Phys. 30, 2132 (1989)] is developed for the complete set of interactions of the Dirac particle. The essence of the method consists of the separation of the first-order matrix differential operators that define the dependence of the Dirac bispinor on the related variables, but commutation of such operators with or between the operator of the equation is not assumed. This approach, which is perfectly justified in the presence of gravitational [Theor. Math. Phys. 70, 204 (1987)] or vector fields [J. Math. Phys. 30, 2132 (1989)], permits one to find all the possibilities of separation of variables in the Dirac equation in the case of the most general set of external fields. The complete set of interactions of the Dirac particle is determined by the symmetry group of equations, namely, viz. the SU(4) group. The interactions are scalar, vector, tensor, pseudovector and pseudoscalar. The analysis in this article is limited to Cartesian coordinates. The corresponding results for the general curvilinear coordinates will be presented in a future paper.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529476
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    Paper (German National Licenses)
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