TY - JOUR

T1 - Fields nonlocal in Clifford space. I. Classical gauge-invariant nonlinear field theory

AU - Danos, Michael

AU - Greiner, Walter

AU - Rafelski, Johann

N1 - Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.

PY - 1972

Y1 - 1972

N2 - A fully gauge-invariant, Lorentz-covariant, nonlocal, and nonlinear theory, for coupled spin-1/2 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.

AB - A fully gauge-invariant, Lorentz-covariant, nonlocal, and nonlinear theory, for coupled spin-1/2 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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U2 - 10.1103/PhysRevD.6.3476

DO - 10.1103/PhysRevD.6.3476

M3 - Article

AN - SCOPUS:35949034433

VL - 6

SP - 3476

EP - 3491

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 0556-2821

IS - 12

ER -