Correlators are simpler than wavefunctions

TL;DR

This paper explains why equal-time correlators are simpler than wavefunctions, highlighting their integral structure, pole patterns, and factorization properties, with implications for quantum field theory calculations.

Contribution

It reveals the fundamental reasons behind the simplicity of correlators compared to wavefunctions and explores their properties in various limits and theories.

Findings

Correlators are obtained by integrating Feynman propagators over full spacetime.

Correlators exhibit a systematic Laurent expansion with vanishing first subleading terms.

The expansion around the total energy pole can be understood via a differential operator.

Abstract

Several recent works have revealed a simplicity in equal-time correlators that is absent in their wavefunction counterparts. In this letter, we show that this arises from the simple fact that the correlator is obtained by integrating Feynman propagators over the full spacetime, as opposed to the half-space for the wavefunction. Several striking new properties of correlators for any graph are made obvious from this picture. Certain patterns of poles that appear in the wavefunction do not appear in the correlator. The correlator also enjoys several remarkable factorization properties in various limits. Most strikingly, the correlator admits a systematic Laurent expansion in the neighborhood of every pole, with the first subleading term vanishing for every pole. There is an especially simple understanding of the expansion around the total energy pole up to second order, given by a differential operator acting on the amplitude. Finally, we show how these results extend beyond single graphs to the full correlator in Tr $\phi^3$ theory.