Skip to main content
OSTI.GOVU.S. Department of Energy Office of Scientific and Technical Information
U.S. Department of Energy
Office of Scientific and Technical Information
 

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

Similar Records

Historical development of the Bhabha first-order relativistic wave equations for arbitrary spin
Journal Article · Thu Sep 01 00:00:00 EDT 1977 · Am. J. Phys.; (United States) · OSTI ID:6729260
The Maxwell{endash}Vlasov equations in Euler{endash}Poincar{acute e} form
Journal Article · Mon Jun 01 00:00:00 EDT 1998 · Journal of Mathematical Physics · OSTI ID:624859
Einstein--Maxwell equations and the conformal Ricci collineations
Journal Article · Mon Jun 01 00:00:00 EDT 1987 · J. Math. Phys. (N.Y.); (United States) · OSTI ID:6626754

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