A Note on the Existence of Equal Time Correlators

TL;DR

This paper investigates conditions under which equal time correlators of scalar fields in flat space are finite, identifying cases of divergence and providing criteria for their existence, with applications to various models.

Contribution

It offers new insights into the finiteness and existence conditions of equal time correlators in quantum field theory, including specific examples and models.

Findings

Identifies conditions for finiteness of correlators

Provides criteria for correlator existence after renormalization

Analyzes examples like λφ^4 model and effective field theories

Abstract

The Schroedinger picture, which underpins the Wavefunction of the Universe framework to compute Cosmological Correlators, is known to be generically problematic in QFT because of the required infinite localization of the fields in time. We study under which conditions momentum space equal time correlators of scalar fields are finite in flat space. We identify cases where they can be divergent even after renormalizing the theory, while also providing sufficient conditions for their existence. Concrete examples are discussed, covering the well known $\lambda\phi^4$ model, composite operators and effective field theories.