S-Matrix Path Integral Approach to Symmetries and Soft Theorems

TL;DR

This paper presents a path integral formulation of the S-matrix that emphasizes asymptotic data, simplifying derivations of soft theorems and enabling efficient calculations in curved spacetime.

Contribution

It introduces a path integral approach to the S-matrix based on asymptotic data, connecting soft theorems to symmetry invariance and facilitating computations in curved backgrounds.

Findings

Soft photon theorem derived from large gauge invariance.

Formalism simplifies soft theorem derivations.

Enables efficient S-matrix calculations in curved spacetime.

Abstract

We explore a formulation of the S-matrix in terms of the path integral with specified asymptotic data, as originally proposed by Arefeva, Faddeev, and Slavnov. In the tree approximation the S-matrix is equal to the exponential of the classical action evaluated on-shell. This formulation is well-suited to questions involving asymptotic symmetries, as it avoids reference to non-gauge/diffeomorphism invariant bulk correlators or sources at intermediate stages. We show that the soft photon theorem, originally derived by Weinberg and more recently connected to asymptotic symmetries by Strominger and collaborators, follows rather simply from invariance of the action under large gauge transformations applied to the asymptotic data. We also show that this formalism allows for efficient computation of the S-matrix in curved spacetime, including particle production due to a time dependent metric.