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New and old symmetries of the Maxwell and Dirac equations

Journal Article · · Sov. J. Particles Nucl. (Engl. Transl.); (United States)
OSTI ID:5833932
;

The symmetry properties of Maxwell's equations for the electromagnetic field and also of the Dirac and Kemmer-Duffin-Petiau equations are analyzed. In the framework of a ''non-Lie'' approach it is shown that, besides the well-known invariance with respect to the conformal group and the Heaviside-Larmor-Rainich transformations, Maxwell's equations have an additional symmetry with respect to the group U(2)xU(2) and with respect to the 23-dimensional Lie algebra A/sub 23/. The transformations of the additional symmetry are given by nonlocal (integro-differential) operators. The symmetry of the Dirac equation in the class of differential and integro-differential transformations is investigated. It is shown that this equation is invariant with respect to an 18-parameter group, which includes the Poincare group as a subgroup. A 28-parameter invariance group of the Kemmer-Duffin-Petiau equation is found. Finite transformations of the conformal group for a massless field with arbitrary spin are obtained. The explicit form of conformal transformations for the electromagnetic field and also for the Dirac and Weyl fields is given.

Research Organization:
Institute of Mathematics, Ukrainian Academy of Sciences, Kiev
OSTI ID:
5833932
Journal Information:
Sov. J. Particles Nucl. (Engl. Transl.); (United States), Journal Name: Sov. J. Particles Nucl. (Engl. Transl.); (United States) Vol. 14:1; ISSN SJPNA
Country of Publication:
United States
Language:
English

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Related Subjects

645400* -- High Energy Physics-- Field Theory
657007 -- Electricity & Magnetism-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CONFORMAL INVARIANCE
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
ELECTRODYNAMICS
ELECTROMAGNETIC FIELDS
EQUATIONS
INVARIANCE PRINCIPLES
LIE GROUPS
MAXWELL EQUATIONS
PARTIAL DIFFERENTIAL EQUATIONS
SYMMETRY
SYMMETRY GROUPS
U GROUPS
U-2 GROUPS
WAVE EQUATIONS