New and old symmetries of the Maxwell and Dirac equations
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), Vol. 14:1
- Country of Publication:
- United States
- Language:
- English
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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DIRAC EQUATION
CONFORMAL INVARIANCE
SYMMETRY
MAXWELL EQUATIONS
ELECTRODYNAMICS
ELECTROMAGNETIC FIELDS
U-2 GROUPS
WAVE EQUATIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
INVARIANCE PRINCIPLES
LIE GROUPS
PARTIAL DIFFERENTIAL EQUATIONS
SYMMETRY GROUPS
U GROUPS
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