Physics
Scientific paper
Jun 1985
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985phrvd..31.3090n&link_type=abstract
Physical Review D (Particles and Fields), Volume 31, Issue 12, 15 June 1985, pp.3090-3098
Physics
6
Gravity In More Than Four Dimensions, Kaluza-Klein Theory, Unified Field Theories, Alternative Theories Of Gravity
Scientific paper
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 R1 affine gauge potentials. Solutions of Newton's second law then define R1 affine energy geodesics, and the R1 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 R4 affine four-vectors. If this R4 affine structure is to be compatible with the O(1,3) Riemannian structure of spacetime, then the R4 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) ×R4 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.
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