Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction to relativistic quantum mechanics
- 2 The Klein–Gordon equation
- 3 The Dirac equation
- 4 Quantization of the non-relativistic string
- 5 Introduction to relativistic quantum field theory: propagators, interactions, and all that
- 6 Quantization of the Klein–Gordon field
- 7 Quantization of the Dirac field
- 8 Maxwell's equations and quantization of the electromagnetic field
- 9 The electromagnetic Lagrangian and introduction to Yang–Mills theory
- 10 Asymptotic fields and the LSZ formalism
- 11 Perturbation theory
- 12 Elementary processes of quantum electrodynamics
- 13 Introduction to regularization, renormalization, and radiative corrections
- Appendix A A brief survey of group theory and its notation
- Bibliography
- Index
10 - Asymptotic fields and the LSZ formalism
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- 1 Introduction to relativistic quantum mechanics
- 2 The Klein–Gordon equation
- 3 The Dirac equation
- 4 Quantization of the non-relativistic string
- 5 Introduction to relativistic quantum field theory: propagators, interactions, and all that
- 6 Quantization of the Klein–Gordon field
- 7 Quantization of the Dirac field
- 8 Maxwell's equations and quantization of the electromagnetic field
- 9 The electromagnetic Lagrangian and introduction to Yang–Mills theory
- 10 Asymptotic fields and the LSZ formalism
- 11 Perturbation theory
- 12 Elementary processes of quantum electrodynamics
- 13 Introduction to regularization, renormalization, and radiative corrections
- Appendix A A brief survey of group theory and its notation
- Bibliography
- Index
Summary
In this chapter, the Lehmann–Symanzik–Zimmermann (LSZ) formalism is presented. This was developed in 1955 and is named after its inventors, namely, the three German physicists H. Lehmann, K. Symanzik, and W. Zimmermann. Especially, the LSZ formalism includes the LSZ reduction formula that provides an explicit way of expressing physical S matrix elements (i.e. scattering amplitudes) in terms of T-ordered correlation functions of an interacting field within a quantum field theory to all orders in perturbation theory. Thus, the goal is to express the S matrix elements in terms of asymptotic free fields instead of the unknown interacting field. Therefore, given the Lagrangian of some quantum field theory, it leads to predictions of measurable quantities. Note that the LSZ reduction formula cannot treat massless particles, bound states, and so-called topological defects. For example, in quantum chromodynamics (QCD), the asymptotic states are bound, which means that they are not free states. However, the original formula can be generalized in order to include bound states, which are states described by non-local composite fields. In addition, in statistical physics, a general formulation of the fluctuation–dissipation theorem, which is a theorem that can be used to predict the non-equilibrium behaviour of a system, can be obtained using the LSZ formalism.
- Type
- Chapter
- Information
- Relativistic Quantum PhysicsFrom Advanced Quantum Mechanics to Introductory Quantum Field Theory, pp. 188 - 196Publisher: Cambridge University PressPrint publication year: 2011