a generally covariant generalization of the dirac equation that does not require gauges

Abstract: In that regard Dirac in 1928 made his equation(1) flat space(2). But space is not in general flat, there are forces.

So over the past 100 years people have had to try to make up for that mistake by adding adhoc convoluted gauge force after gauge force until theoretical physics became a mass of confusion, a train wreck, a junk pile. So all they can do for ever and ever is to rearrange that junk pile with zero actual progress in fundamental theoretical physics being made,.. forever.

By the way note that Newpde (3) γ^μ√κ_μμ(∂ψ/∂x_μ)=(ω/c)ψ is NOT flat space (4) so it cures this problem (5).



References

(1) γ^μ(∂ψ/∂x_μ)=(ω/c)ψ

(2) Spherical symmetry: (γ^x√κ_xxdx+γ^y√κ_yydy+γ^z√κ_zzdz+γ^t√κ_ttidt)²=κ_xxdx²+κ_yydy²+κ_zzdz²-κ_ttdt²

κ_xx=κ_yy=κ_zz=κ_tt=1 is flat space, Minkowski, as in his (above) Dirac equation.

(3) γ^μ√κ_μμ(∂ψ/∂x_μ)=(ω/c)ψ for e,v. So we didn’t just drop the κ_μν.

(4)Here κ_oo=1-r_H/r =1/κ_rr. r_H=2e²/mc². This New pde, with this κ_μν is derived from an Occam’s razor motivated assumption: postuate1↔Newpde.

(5) In fact the third order Taylor expansion terms of that square root (√κ_μν) provide the Lamb shift and anomalous gyromagnetic ratio without the renormalization and infinities. The κ_μνalso provides the general covariance of the Newpde. Also the New pde composite 3e and composite e,v give us particle physics: the particle multiplets and Standard electroweak Model(SM) respectively.