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Scattering in relativistic quantum field theory: basic concepts, tools, and results

Detlev Buchholz, Wojciech Dybalski

Abstract

We provide an overview of basic concepts, tools, and results of quantum field theoretical scattering theory. This article is prepared for the second edition of the Encyclopedia of Mathematical Physics, edited by M. Bojowald and R.J. Szabo, to be published by Elsevier.

Scattering in relativistic quantum field theory: basic concepts, tools, and results

Abstract

We provide an overview of basic concepts, tools, and results of quantum field theoretical scattering theory. This article is prepared for the second edition of the Encyclopedia of Mathematical Physics, edited by M. Bojowald and R.J. Szabo, to be published by Elsevier.

Paper Structure

This paper contains 7 sections, 5 theorems, 31 equations.

Table of Contents

  1. Physical Motivation and Mathematical Setting
  2. Haag-Ruelle Theory
  3. LSZ Formalism
  4. Asymptotic Particle Counters
  5. Massless particles and Huygens' principle
  6. Beyond Wigner's Concept of Particle
  7. Asymptotic completeness

Key Result

Theorem 1

Consider a theory of a particle of mass $m > 0$ which satisfies the standing assumptions and the stability condition (herbst). Then there exist canonical isometries $\Omega^{{\textnormal{\tiny in}} / {\textnormal{\tiny out}}}$, mapping the Fock space ${\cal H}_F$ based on the single-particle space $

Theorems & Definitions (5)

  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Theorem 4
  • Theorem 5