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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik
MP 10: Quantum Field Theory: gauge theories
MP 10.1: Vortrag
Mittwoch, 1. April 2020, 12:00–12:20, H-HS VII
Perturbative construction of a string-localized Dirac field in a Hilbert space representation of QED — A program. — •Jens Mund1, Karl-Henning Rehren2, and Bert Schroer3 — 1Universidade Federal de Juiz de Fora, Brazil — 2Georg-August Universität Göttingen, Deutschland — 3CBPF, Rio de Janeiro, Brazil
The construction of charged sectors in QED has been a difficult task due to the infrared problems related to Gauss law, implying that the Dirac field cannot be point-like localized and that the electron is an infra-particle.
We propose a novel strategy for a straightforward perturbative construction of QED along the lines of Epstein and Glaser, which complies with these features, and also with positivity. Our interacting Dirac field is not point- but “string-localized”, i.e., localized on half-rays extending to space-like infinity. The construction works in a framework which relates the free (Gupta-Bleuler) vector potential acting in a Krein space with its string-localized version acting in the physical subspace. As input for the interacting Dirac field we use the free string-localized “dressed Dirac field” :exp(iqφ)ψ:, where q is the electron charge, and φ is the (known) field that implements the gauge transformation between the two potentials. The free dressed Dirac field already describes the electron as an infra-particle.
We hope that this model can be renormalized at all orders, such that the mentioned features hold (positivity, Gauss’ law, infra-particle aspect). Restricting to the forward light cone and using light-like string directions, the infra-particle aspect might disappear.