A New invariant ds=ds$_{t}$+ds$_{\phi}$ in the String Theory Action Leads to Replacing The General Covariance In the SM Dirac Equation Gauge Derivatives With An Equivalent General Covariance In The Metric That This Dirac Equation is Derived From
ORAL
Abstract
Substituting the invariant ds=ds$_{t}$+ds$_{\phi }$ into the string theory action gives a cross term 2ds$_{t}$ds$_{\phi }$ (ds was squared in finding the string theory action area) implying spin thus requiring linearization of a diagonized ds$^{2}$. Here ds$_{t}=\surd $g$_{oo}$dt This linearization replaces ds=ds$_{t}$+ds$_{\phi }$ with a matrix ds=$\alpha _{t}$ds$_{t}+\alpha _{\phi }$ds$_{\phi }$ and thereby replaces the general covariance in the gauge derivatives in the Standard Model (SM) with a general covariance in the\textit{ original} metric (given that ds$_{t}=\surd $g$_{oo}$dt) that is used to start the derivation of the SM Dirac equation. This puts in the general covariance at the very beginning of the Dirac equation derivation, \textit{where it belongs}. The result is a new Dirac equation ($\surd $\textbf{\textit{g}}$_{\mu \mu }$\textit{$\gamma $}$_{\mu }$\textit{$\partial \psi $/$\partial $x}$_{\mu }$\textit{+i$\omega \psi $=0 }with\textbf{~}\textbf{g}$_{oo}$=1-2e$^{2}$/rm$_{e}$c$^{2}$=1-r$_{H}$/r) that does not require the covariant gauge derivatives anymore but yet still \textit{retains }the general covariance creating a \textbf{ONE} free parameter theory, instead of 18 of the SM. For example this new Dirac equation has a singularity-stability radius r$_{H}$ and, because of equivalence principle considerations, is allowed only \textit{one} type of charge e. Thus near r$_{H}$ the 2P$_{3/2}$ state for this new Dirac equation gives a $\psi ^{tt}\psi $ azimuthal trifolium, 3 lobe shape; so this ONE charge e (so don't need \textbf{ color} to guarantee this) spends \textbf{1/3} of its time in each lobe (\textbf{fractionally charged} lobes), the lobe structure is locked into the center of mass \textbf{(asymptotic freedom}), there are\textbf{ six} 2P states (corresponding to the 6 flavors) ;~ which are the~~\textbf{main properties of quarks}!~ Thus we end up with the experimental implications of the Standard Model (SM) by postulating just ONE particle with mass and string theory finally then exchanges its excessive generality for a Ockam's razor optimized theory.
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Authors
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Joel Maker
PRA