László András (Wigner FK): On generally covariant mathematical formulation of Feynman integral in Lorentz signature

Friday 7 Oct 2022, 14:00 → 15:00 Europe/Budapest

Tanacsterem

Feynman integral is one of the most promising methodologies for defining a generally covariant formulation of nonperturbative interacting quantum field theories (QFTs) without a fixed prearranged causal background. Recent literature indicates that in such scenario, one needs to consider the problematics in the original Lorentz signature. Lorentz signature Feynman integrals are known, however, to be mathematically ill-defined. The Feynman integral formulation has, however, a differential reformulation: the master Dyson-Schwinger (MDS) equation for field correlators. In this talk we show that with the right choice of variables, the MDS equation is mathematically well defined: the involved function spaces and operators can be defined and their properties can be established. Therefore, MDS equation can serve as a substitute for the Feynman integral, in a mathematically sound formulation of constructive QFT, in arbitrary signature, without a fixed background causal structure. It is also shown that the Wilsonian regularization of the MDS equation can be canonically defined. Our main result is a necessary and sufficient condition for the regularized MDS solution space to be nonempty, which also provides a convergent iterative approximation for the solution. The talk is based on the paper: Class. Quant. Grav. 39 (2022) 185004.

elmo.pdf