QFT on compact metric-measure spaces

Develop a mathematically precise definition and framework for quantum field theories when the underlying spacetime is an arbitrary compact metric-measure space, extending beyond smooth manifolds.

Background

The paper advocates treating moduli of QFTs via metric geometry and measured Gromov–Hausdorff limits, motivating a notion of QFTs on general compact metric-measure spaces rather than only smooth manifolds.

Such a formulation is necessary to analyze degenerations and compactifications of moduli, but a concrete definition is still lacking; the Appendix sketches preliminary ideas.