Fields nonlocal in Clifford space. I. Classical Gauge-invariant nonlinear field theory

  • A fully gauge-invariant, Lorentz-covariant, nonlocal, and nonlinear theory, for coupled spin-½ fields, ψ, and vector fields, A, i.e., "electrons" and "photons," is constructed. The field theory is linear in the ψ fields. The nonlinearity in the A fields arises unambiguously from the requirement of gauge invariance. The coordinates are generalized to admit hypercomplex values, i.e., they are taken to be Clifford numbers. The nonlocality is limited to the hypercomplex component of the coordinates. As the size of the nonlocality is reduced toward zero, the theory goes over into the inhomogeneous Dirac theory. The nonlocality parameter corresponds to an inverse mass and induces self-regulatory properties of the propagators. It is argued that in a gauge-invariant theory a graph-by-graph convergence is impossible in principle, but it is possible that convergence may hold for the complete solution, or for sums over classes of graphs.

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Author:Michael Danos, Walter GreinerGND, Johann RafelskiORCiDGND
Parent Title (German):Physical review D
Document Type:Article
Date of Publication (online):2006/06/26
Year of first Publication:1972
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2006/06/26
Page Number:16
First Page:3476
Last Page:3491
Institutes:Physik / Physik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
Licence (German):License LogoDeutsches Urheberrecht