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 .   ${\displaystyle g}$

The perturbation theory is successfully applied where the coupling constant is small ( ) and so the series converges : ${\displaystyle g\ll 1}$

• 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

• Lattice theory
• Dyson-Schwinger equations

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 .