Einstein-Maxwell dynamics as a P(4) affine theory
In Newtonian mechanics the energy of a particle is defined only up to an arbitrary additive constant. By using affine functions to model the Newtonian energy we show that it is possible to reformulate arbitrary time- and velocity-independent forces as R/sup 1/ affine gauge potentials. Solutions of Newton's second law then define R/sup 1/ affine energy geodesics, and the R/sup 1/ flat gauge potentials are shown to correspond to conservative Newtonian forces. We generalize these ideas to relativistic mechanics by modeling the energy-momentum of classical particles as R/sup 4/ affine four-vectors. If this R/sup 4/ affine structure is to be compatible with the O(1,3) Riemannian structure of spacetime, then the R/sup 4/ gauge potential must correspond to an antisymmetric tensor field on spacetime, and this field is identified with the electromagnetic field tensor. We are eventually led to a reformulation of the Einstein-Maxwell theory as a P(4) = O(1,3) x R/sup 4/ affine gauge theory in which the timelike affine geodesics correspond to Lorentz-force-law trajectories, and the Einstein-Maxwell field equations are reformulated as gauge field equations in terms of the P(4) curvature.
- Research Organization:
- Department of Mathematics, Box 8205, North Carolina State University, Raleigh, North Carolina 27695-8205
- OSTI ID:
- 5668905
- Journal Information:
- Phys. Rev. D; (United States), Journal Name: Phys. Rev. D; (United States) Vol. 31:12; ISSN PRVDA
- Country of Publication:
- United States
- Language:
- English
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