New Generally Covariant Generalization of the Dirac Equation Not Requiring Gauges
ORAL
Abstract
We introduce a new pde ($\Sigma _{\mu }\surd \kappa _{\mu \mu }$\textit{$\gamma $}$_{\mu }$\textit{$\partial \psi $/$\partial $x}$_{\mu }$\textit{-$\omega \psi $=0}) with spherically symmetric diagonalized $\kappa _{00}$ = 1-r$_{H}$/r=1/$\kappa _{rr}$ giving it general covariance. If r$_{H}$ =2e$^{2}$/m$_{e}$c$^{2}$ this new pde reduces to the standard Dirac equation as r$\to \infty $. Next we solve this equation directly using separation of variables (e.g., 2P, 2S, 1S terms). Note metric time component $\kappa _{oo}$ =0 at r=r$_{H}$ and so clocks slow down with \textit{baryon stability} the result. Note also that near r$_{H}$ the 2P$_{3/2}$ state for this new Dirac equation gives a azimuthal trifolium, 3 lobe shape; so this \textbf{ONE} charge$ e$ (so don't need \textit{color} to guarantee this) spends $1/3$ of its time in each lobe (\textit{fractionally charged} lobes), the lobe structure is locked into the center of mass \textbf{(}\textit{asymptotic freedom}), there are \textit{six }2P states (corresponding to the 6 flavors);~the P wave scattering gives the \textit{jets}\textbf{,} all these properties together constituting the~\textit{main properties of quarks!}~without invoking the many free parameters, gauge conditions of QCD. Also the 2S$_{1/2}$ is the\textbf{ }\textit{tauon} and the 1S$_{\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} }$is the \textit{muon} here. The S matrix of this new pde gives the \textit{W and Z as resonances and does not require renormalization counterterms or free parameters. } Thus we get nuclear, weak and E{\&}M phenomenology as\textit{ one} step solutions of this new pde.
Authors
-
David Maker
None, PRA