TL;DR
This paper explores the path-integral approach to quantum cosmology with a scalar field, analyzing two-point functions and their properties within loop quantum cosmology, and clarifying their physical interpretations.
Contribution
It provides a comprehensive overview of two-point functions in quantum cosmology, including vertex expansions and composition laws, with insights into their physical significance.
Findings
Derived vertex expansions for two-point functions.
Clarified the relation between group averaging and deparametrised frameworks.
Discussed implications for single universe and multiverse theories.
Abstract
We discuss the path-integral formulation of quantum cosmology with a massless scalar field as a sum-over-histories, with particular reference to loop quantum cosmology. Exploiting the analogy with the relativistic particle, we give a complete overview of the possible two-point functions, deriving vertex expansions and composition laws they satisfy. We clarify the tie between definitions using a group averaging procedure and those in a deparametrised framework. We draw some conclusions about the physics of a single quantum universe and multiverse field theories where the role of these sectors and the inner product are reinterpreted.
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