I am presently working on a paper to show how electrodynamic gauge theory can be directly connected to generally-covariant gravitational theory. In essence, we show how there is a naturally occurring gauge parameter in gravitational gemometrodynamics which can be directly connected with the gauge parameter used in electrodynamics, while at the same time local gauge transformations acting on fermion wavefunctions may be synonymously described as general coordinate transformations acting on those same fermion wavefunctions.
This is linked below, and I will link updates as they are developed.
Inferring Electrodynamic Gauge Theory from General Coordinate Invariance
If you check out sci.physics.foundations and sci.physics.research, you will see the rather busy path which I have taken over the last month to go from baryons and confinement to studying the Heisenberg equation of motion and Ehrenfest’s theorem, to realizing that there was an issue of interest in the way that Fourier kernels behave under general coordinate transformations given that a general coordinate x^u is not itself a generally-covariant four vector. Each step was a “drilling down” to get at underlying foundational issues, and this paper arrives at the most basic, fundamental underlying level.
Looking forward to your feedback.
Jay
Lab Notes for a Scientific Revolution (Physics) 