Spatially asymptotic S-matrix from general boundary formulation

TL;DR

This paper introduces a novel spatially asymptotic S-matrix in quantum field theory, applicable when interactions diminish with distance but persist over time, and demonstrates its equivalence to the traditional S-matrix.

Contribution

It develops a new S-matrix framework based on the general boundary formulation, shifting the asymptotic states from temporal to spatial infinity, and shows their equivalence.

Findings

The new S-matrix is equivalent to the traditional one in applicable scenarios.

Explicit expressions for the S-matrix are derived using coherent states.

Crossing symmetry is manifest in the new formalism.

Abstract

We construct a new type of S-matrix in quantum field theory using the general boundary formulation. In contrast to the usual S-matrix the space of free asymptotic states is located at spatial rather than at temporal infinity. Hence, the new S-matrix applies to situations where interactions may remain important at all times, but become negligible with distance. We show that the new S-matrix is equivalent to the usual one in situations where both apply. This equivalence is mediated by an isomorphism between the respective asymptotic state spaces that we construct. We introduce coherent states that allow us to obtain explicit expressions for the new S-matrix. In our formalism crossing symmetry becomes a manifest rather than a derived feature of the S-matrix.