Coherent mathematical framework for the Feynman path integral in physically relevant QFT

Establish a coherent mathematical framework for the Feynman path integral applicable to physically relevant quantum field theories, particularly in curved spacetimes, thereby reconciling geometric approaches with rigorous measure-theoretic formulations.

Background

The thesis motivates a geometric Hamiltonian approach to QFT on curved spacetimes and contrasts it with algebraic and path-integral methods. The authors identify the path integral as a central object whose rigorous formulation would bridge geometric insight and quantum field theory.

While the literature contains many attempts at a rigorous path-integral formulation, the authors emphasize that for physically relevant theories a satisfactory, generally applicable framework is still missing, and they frame this as a key outstanding issue that motivates their work.