Local Properties of Measures in Quantum Field Theory and Cosmology

TL;DR

This paper explores measure theoretical properties in quantum field theory and cosmology, establishing analogies between measures on generalized connections and the Bohr compactification, and characterizing measures in scalar field quantization.

Contribution

It introduces new measure-theoretic results linking quantum geometry measures with those in cosmological models and scalar field quantization.

Findings

Analogous measure properties in generalized connections and Bohr compactification

Characterization of support of measures in scalar field quantization

Connections between quantum geometry and cosmological measures

Abstract

We show that measure theoretical results concerning the Ashtekar-Lewandowski measure in the space of generalized connections have direct analogues in the context of the Bohr compactification of the line and associated Haar measure. We present also a characterization of the support of the measure associated with the canonical quantization of the free massive scalar field, following closely well known analogous results concerning the Euclidean path integral measure.