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

Michael Danos, Walter Greiner, Johann Rafelski

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)3476-3491
Number of pages16
JournalPhysical Review D
Issue number12
StatePublished - 1972

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)


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