Quantum Scattering Theory in the light of an exactly solvable model with rearrangement collisions

TL;DR

This paper introduces an exactly solvable quantum field theory model with rearrangement collisions, challenging standard assumptions in quantum scattering theory and proposing a new formalism to address these issues.

Contribution

It provides an exactly solvable model demonstrating non-orthogonality of basis states and proposes a new scattering formalism to overcome existing limitations.

Findings

Demonstrates non-orthogonality of basis states in the model

Shows standard assumptions like isometry of M"oller matrix do not hold

Proposes a generalized scattering theory formalism

Abstract

We present an exactly solvable quantum field theory which allows rearrangement collisions. We solve the model in the relevant sectors and demonstrate the orthonormality and completeness of the solutions, and construct the S-matrix. In the light of the exact solutions constructed, we discuss various issues and assumptions in quantum scattering theory, including the isometry of the M\"oller wave matrix, the normalization and completeness of asymptotic states, and the non-orthogonality of basis states. We show that these common assertions do not obtain in this model. We suggest a general formalism for scattering theory which overcomes these, and other, shortcomings and limitations of the existing formalisms in the literature.