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- W2887212634 abstract "We show that in the presence of the torsion tensor $S^k_{phantom{k}ij}$, whose existence is required by the consistency of the conservation law for the total angular momentum of a Dirac particle in curved spacetime with relativistic quantum mechanics, the quantum commutation relation for the four-momentum is given by $[p_i,p_j]=2ihbar S^k_{phantom{k}ij}p_k$. We propose that this relation replaces the integration in the momentum space in Feynman diagrams with the summation over the discrete momentum eigenvalues. We derive a prescription for this summation that agrees with convergent integrals: [ intfrac{d^4p}{(p^2+Delta)^s}rightarrow 4pi U^{s-2}sum_{l=1}^infty int_0^{pi/2} dphi frac{sin^4phi,n^{s-3}}{[sinphi+UDelta n]^s}, ] where $n=sqrt{l(l+1)}$ and $1/sqrt{U}$ is a constant on the order of the Planck mass, determined by the Einstein-Cartan theory of gravity. We show that this prescription regularizes ultraviolet-divergent integrals in loop diagrams. We extend this prescription to tensor integrals and apply it to vacuum polarization. We derive a finite, gauge-invariant vacuum polarization tensor and a finite running coupling that agrees with the low-energy limit of the standard quantum electrodynamics. Including loops from all charged fermions, we find a finite value for the bare electric charge of an electron: $approx -1.22,e$. Torsional regularization, originating from the noncommutativity of the momentum and spin-torsion coupling, therefore provides a realistic, physical mechanism for eliminating infinities in quantum field theory: quantum electrodynamics with torsion is ultraviolet complete." @default.
- W2887212634 created "2018-08-22" @default.
- W2887212634 creator A5017028948 @default.
- W2887212634 date "2017-12-28" @default.
- W2887212634 modified "2023-09-27" @default.
- W2887212634 title "Uncertainty principle for momentum, torsional regularization, and bare charge" @default.
- W2887212634 hasPublicationYear "2017" @default.
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