Authors: Jay R. Yablon
We develop a linear metric element ds in ordinary four-dimensional spacetime which, when held stationary under worldline variations, leads to the gravitational equations of geodesic motion extended to include the Lorentz force law for both abelian and non-abelian gauge fields. We see that in the presence of an electromagnetic vector potential A^µ, all that is needed to obtain this result is to follow the well-known gauge theory prescription of replacing the kinetic momentum p^µ with a canonical momentum π^µ=p^µ+eA^µ in the mass / momentum relationship m^2=p_σp^σ, and then to apply variational calculus to obtain the motion of charged particles in this potential. We also show how by this same prescription, Maxwell’s classical source-free field equations become embedded within canonical extensions of the Riemann tensor and the gravitational field equation.
Comments: 13 Pages. v5 modifies section 4 to cover electrodynamics with non-zero electric charge sources.
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[v1] 2015-12-30 13:28:51
[v2] 2015-12-31 13:07:25
[v3] 2016-01-01 23:00:44
[v4] 2016-01-03 09:42:54
[v5] 2016-01-05 00:33:45
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