# Perturbation theory (quantum field theory)

The **perturbation in the quantum field theory** is a method in the processes that lead to a specific element of the S matrix according to the number of occurring in this process contribute interactions are rated. The corresponding Feynman diagrams are drawn for all processes up to a certain order, a mathematical expression is assigned to them and an estimate of the process up to the given order is obtained by adding all the terms . This corresponds to a series expansion in the coupling constant .

The perturbation theory is successfully applied where the coupling constant is small ( ) and so the series converges :

- in quantum electrodynamics
- in quantum chromodynamics for high energies (coupling constant small thanks to asymptotic freedom ).

## meaning

For a long time, perturbative (or perturbative) calculations were the only access to quantum field theories, since the computer-technical requirements for non-perturbative calculations were not yet met.

However, this is the case today, and so non-perturbation-theoretical approaches are now also being chosen in current research in order to penetrate into areas in which the coupling constant *cannot* be assumed to be small, for example in the low- energy range of quantum chromodynamics and for collective excitations in solids .

Bonding states in principle elude a perturbative description, since their constituents interact infinitely often by definition.

## See also

## literature

Perturbation theory is covered in most introductory books on quantum field theories. Some of the following are mentioned here:

- Michael Peskin and Daniel Schröder: Introduction to Quantum Field Theory . Westview Press, Boulder, Col. 2007, ISBN 978-0-201-50397-5 (English).
- Lewis Ryder: Quantum field theory . Cambridge 1996, ISBN 978-0-521-47814-4 .
- Walter Greiner u. a .: Theoretical physics . Quantum electrodynamics. tape 7 . Verlag Harri Deutsch, 1994, ISBN 978-3-8171-1426-9 .
- Walter Greiner u. a .: Theoretical physics . Field quantization. tape 7 a. Verlag Harri Deutsch, 1993, ISBN 978-3-87144-975-8 .
- Walter Greiner u. a .: Theoretical physics . Gauge theory of weak interaction. tape 8 . Verlag Harri Deutsch, 1994, ISBN 978-3-8171-1426-9 .
- Walter Greiner u. a .: Theoretical physics . Quantum chromodynamics. tape 10 . Verlag Harri Deutsch, 1994, ISBN 978-3-8171-1618-8 .