Geometrical unified theory of connection fields and frame fields

Journal Article · Sun Feb 15 04:00:00 EST 1987 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.35.1225· OSTI ID:7018223

Gonzalez-Martin, G

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

Related Subjects

645400* -- High Energy Physics-- Field Theory
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