# Bulletin of the American Physical Society

# APS April Meeting 2022

## Volume 67, Number 6

## Saturday–Tuesday, April 9–12, 2022; New York

### Session K17: Poster Session II (2:00-4:00 pm)

2:00 PM,
Sunday, April 10, 2022

Room: 9th Floor Terrace

### Abstract: K17.00019 : Generally Covariant Generalization of The Dirac Equation (a new pde) That Does Not Require Gauges

#### Presenter:

Joel D Maker

#### Author:

Joel D Maker

Toward the end of his life Dirac tried to modify his equation so that it did not require the clunky infinities and a 10

Instead of linearizing a flat space Minkowski metric as Dirac did to get his Clifford algebra, leave it as a point source Schwarzschild metric splitting r

So divide

We get an equivalence principle for

^{96}gram/cm^{3}vacuum density to get the correct Lamb shift and gyromagnetic ratio. Well, it is easy to fix this problem.Instead of linearizing a flat space Minkowski metric as Dirac did to get his Clifford algebra, leave it as a point source Schwarzschild metric splitting r

_{H}in 1-r_{H}/r=_{oo}into r_{H}= 2GM/c^{2 }and r_{H}=2e^{2}/m_{L}c^{2}instead of just 2GM/c^{2}and so maintaining a*general covariance*for the (Lepton: m_{L}= m+m+m_{e}) Dirac equation.So divide

_{xx}dx^{2 }+_{yy}dy^{2}+_{zz}dz^{2}+_{tt}dt^{2}=ds^{2 }by ds^{2}and define p_{x}=dx/ds and we find using the Dirac gammas and plugging in the operator formalism and we get a generally covariant m_{L}pde. In spherical coordinates the energy turns out to be E=1/_{tt}=1/(1-r_{H}/r)^{.5}=1+r_{H}/2r-(**3/8)(r**+.. 1+V_{H}/r)^{2}_{c}-V+... After multiplying (this normalized) E by m_{L}c^{2}we note the first term is lepton mass energy, V_{C}is the usual Coulomb potential energy and we split off the electron component m_{e}c^{2}in E and get for the 3^{rd}term:_{2,0,0}*V_{2,0,0}dV=E=Lamb shift(eq.6.12.1, PartI, DavidMaker.com) =h27MHz component.We get an equivalence principle for

_{ij}by assuming the only particle with nonzero rest mass is the electron (with the baryons 2P_{3/2}, 2P_{½}composites and , S_{½}excited states, PartI) and that splitting of r_{H}into separate r_{HN+1}=2GM/c^{2}and r_{HN}=2e^{2}/m_{L}c^{2 }comes from a cosmological and electron selfsimilar (fractal) universality of this new Lepton pde.
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