Geometrical unified theory of connection fields and frame fields
A theory of connections on a principal bundle with structure group SL(4,R), the highest-dimensional simple subgroup of the Clifford algebra associated with a space-time of signature (1,-1,-1,-1), is used to interpret Dirac's equation geometrically. The proposed theory unifies Dirac's equation with the equations of gravitation and electrodynamics. The Lorentz equation of motion for charges is a consequence of the field equations when the connection reduces to a component which may be identified as the electromagnetic field. If this part of the generalized connection does not vanish, we obtain the correct expression for the electric current in terms of spinors and the correct minimal coupling in the first nonrelativistic approximation.
- Research Organization:
- Departamento de Fisica, Universidad Simon Bolivar, Apartado 80659, Caracas 1080, Venezuela
- OSTI ID:
- 7018223
- Journal Information:
- Phys. Rev. D; (United States), Journal Name: Phys. Rev. D; (United States) Vol. 35:4; ISSN PRVDA
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
ELECTRODYNAMICS
ELECTROMAGNETIC FIELDS
EQUATIONS
FIELD EQUATIONS
FIELD THEORIES
GRAVITATIONAL FIELDS
LIE GROUPS
PARTIAL DIFFERENTIAL EQUATIONS
SL GROUPS
SPACE-TIME
SPINORS
SYMMETRY GROUPS
UNIFIED-FIELD THEORIES
WAVE EQUATIONS