From Amplitudes to Analytic Wavefunctions

TL;DR

This paper introduces an amplitude representation for the flat space wavefunction, enabling the classification of its singularities and providing insights into its analytic structure relevant for boundary observables in cosmology.

Contribution

It develops a novel amplitude-based integral representation of the wavefunction, separating amplitude and subleading parts, and classifies wavefunction singularities into amplitude-like and wavefunction-specific types.

Findings

Wavefunction can be expressed as an amplitude-like integral with an energy-fixing kernel.

Singularities are classified into amplitude-type and wavefunction-type.

Analysis of tree level and one-loop scalar diagrams reveals detailed singularity structures.

Abstract

The field-theoretic wavefunction has received renewed attention with the goal of better understanding observables at the boundary of de Sitter spacetime and studying the interior of Minkowski or general FLRW spacetime. Understanding the analytic structure of the wavefunction potentially allows us to establish bounds on physical observables. In this paper we develop an amplitude representation for the flat space wavefunction, which allow us to write the flat space wavefunction as an amplitude-like Feynman integral integrated over an energy-fixing kernel. With this representation it is possible to separate the wavefunction into an amplitude part and a subleading part which is less divergent as the total energy goes to zero. In turn the singularities of the wavefunction can be classified into two sets: amplitude-type singularities, which can be mapped to singularities found in amplitudes (including anomalous thresholds), and wavefunction-type singularities, which are unique to the wavefunction. As an example we study several tree level and one loop diagrams for scalars, and explore their singularities in detail.