On some aspects of the definition of scattering states in quantum field theory

TL;DR

This paper examines different methods for defining scattering states in quantum field theory, comparing abelian limit and adiabatic switching, and demonstrates their equivalence through calculations in specific models.

Contribution

It analyzes and compares two limiting procedures for defining scattering states in quantum field theory, highlighting their differences and showing their equivalence in practical calculations.

Findings

Significant differences exist between abelian limit and adiabatic switching approaches.

Both methods yield equivalent results in quantum field theoretical models.

Formulas for scattering states are derived and applied to calculate S-matrix elements and energy corrections.

Abstract

The problem of extending quantum-mechanical formal scattering theory to a more general class of models that also includes quantum field theories is discussed, with the aim of clarifying certain aspects of the definition of scattering states. As the strong limit is not suitable for the definition of scattering states in quantum field theory, some other limiting procedure is needed. Two possibilities are considered, the abelian limit and adiabatic switching. Formulas for the scattering states based on both methods are discussed, and it is found that generally there are significant differences between the two approaches. As an illustration of the application and the features of these formulas, S-matrix elements and energy corrections in two quantum field theoretical models are calculated using (generalized) old-fashioned perturbation theory. The two methods are found to give equivalent results.