The Dirac equation in external fields: Variable separation in Cartesian coordinates

Journal Article · Fri Nov 01 04:00:00 EST 1991 · Journal of Mathematical Physics (New York); (United States)

DOI:https://doi.org/10.1063/1.529476· OSTI ID:5242852

Shishkin, G V; Cabos, W D ^[1]

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1. Department of Theoretical Physics, Byelorussian State University, Minsk 220050 (USSR)

The method of separation of variables in the Dirac equation proposed in an earlier work by one of the present authors (J. Math. Phys. {bold 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. {bold 70}, 204 (1987)) or vector fields (J. Math. Phys. {bold 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.

• OSTI ID: 5242852
• Journal Information: Journal of Mathematical Physics (New York); (United States), Journal Name: Journal of Mathematical Physics (New York); (United States) Vol. 32:11; ISSN JMAPA; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANALYTICAL SOLUTION
CARTESIAN COORDINATES
COORDINATES
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
EQUATIONS
LIE GROUPS
MATRICES
PARTIAL DIFFERENTIAL EQUATIONS
POINCARE GROUPS
SPINOR FIELDS
SPINORS
SYMMETRY
SYMMETRY GROUPS
WAVE EQUATIONS