S-matrix at spatial infinity

TL;DR

This paper introduces a novel approach to constructing the S-matrix in quantum field theory that makes crossing symmetry explicit and handles spatially varying interactions, potentially applicable to complex spacetimes.

Contribution

It presents a new method for S-matrix construction that erases the in/out state distinction and is effective in scenarios with spatially weakening interactions.

Findings

Provides a framework for processes with spatially weakening interactions

Enables S-matrix construction without traditional temporal asymptotic states

Maintains crossing symmetry explicitly

Abstract

We provide a new method to construct the S-matrix in quantum field theory. This method implements crossing symmetry manifestly by erasing the a priori distinction between in- and out-states. It allows the description of processes where the interaction weakens with distance in space, but remains strong in the center at all times. It should also be applicable to certain spacetimes where the conventional method fails due to lack of temporal asymptotic states.