SMuK 2021 – scientific programme

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 18: Constructive Tools for Quantum Field Theory

MP 18.2: Talk

Friday, September 3, 2021, 11:25–11:50, H6

Quantum field theory without ghosts and indefinite metric -- A program and some results. — •Jens Mund — Departamento de Fisica, Universidade Federal de Juiz de Fora, Brazil

Quantum field theories involving interacting vector fields with spin/helicity one (or higher) are usually based on gauge theory: One adds unphysical degrees of freedom in the form of "negative norm" states and "ghost" fields before the construction, and divides them out afterwards by requiring gauge (or BRST) invariance of the S-matrix and of observable fields. The construction of charge-carrying fields (like the Dirac field in QED) is notoriously difficult.

In the talk an alternative approach is presented: Instead of Hilbert space positivity, the localization of (unobservable) fields is weakened, in a way permitted by the principles of relativistic quantum field theory: The fields are localized on "Jordan-Mandelstam strings" extending to space-like infinity. They act in a true Hilbert space without ghosts. In contrast to gauge theory, our approach allows for a direct (perturbative) construction of charged interacting fields. I comment on partial results on (massive and proper) QED, (Abelian) Higgs model, and Yang-Mills models.