Schwingers quantum action principle

Schwinger's quantum action principle , named after its developer Julian Seymour Schwinger , is one of the approaches to quantum field theory . In this formalism, the effect is an operator , unlike in Feynman's path integral formulation, in which the effect is a classical functional . Both approaches are included in the modern formulation of quantum field theory. Historically, Schwinger's approach was the first formulation in which bosons and fermions were treated equally. Feynman, Schwinger and Tomonaga were jointly awarded the Nobel Prize in Physics in 1965 .

The approach is to replace all fields with quantum operators in the classical effect . The principle of action :

${\displaystyle \delta \langle B|A\rangle ={\frac {i}{\hbar }}\langle B|\delta S|A\rangle }$

which stands for the variation according to parameters or parametric functions, then results in the equations of motion of the quantum system . If you vary z. B. after the time in the Bra state , one just gets the time-dependent Schrödinger equation . ${\displaystyle \delta }$ ${\displaystyle \langle B|}$

Historical summary

Between 1951 and 1954 Schwinger wrote a series of six articles in which he built up the quantum field theory based on this principle of variation. At first he called his approach quantum dynamical principle , but already with the second publication he chose the term quantum action principle , which he later retained in his books.

A first application of the operating principle was the derivation of relations between the Green functions of a quantum field theory, which are known today as Dyson-Schwinger equations .

With his approach, Schwinger was also one of the first to be able to treat bosons and fermions together, thus creating a basis for quantum electrodynamics . However, the different approaches to QFT have now merged. In the modern formulation of QFT, the principle of action can be derived from the path integral formalism.

The historical connection between the various approaches to quantum field theory was presented by Silvan S. Schweber , who also summarized the importance of Green's functions in a technical paper.

Individual evidence

1. ↑ ^{a b} J. Schwinger: On Theory of quantized fields I . In: Physical Review . 82, 1951, p. 914. doi : 10.1103 / PhysRev.82.914 .
2. ↑ ^{a b} C. Itzykson, J.-B. Zuber: Quantum Field Theory , McGraw-Hill, 1980. ISBN 0-07-032071-3 . Chapter on functional methods .
3. ↑ ^{a b} J. Schwinger: On Theory of quantized fields II . In: Physical Review . 91, 1953, p. 713. doi : 10.1103 / PhysRev.91.713 .
4. ↑ J. Schwinger: On Theory of Quantized Fields III . In: Physical Review . 91, 1953, p. 728. doi : 10.1103 / PhysRev.91.728 .
5. ↑ J. Schwinger: On Theory of quantized fields IV . In: Physical Review . 92, 1953, p. 1283. doi : 10.1103 / PhysRev.92.1283 .
6. ↑ J. Schwinger: On Theory of quantized fields V . In: Physical Review . 93, 1954, p. 615. doi : 10.1103 / PhysRev.93.615 .
7. ↑ J. Schwinger: On Theory of Quantized Fields VI . In: Physical Review . 94, 1954, p. 1362. doi : 10.1103 / PhysRev.94.1362 .
8. ^ J. Schwinger: On Green's functions of quantized fields I + II . In: PNAS . 37, 1951, pp. 452-459.
9. ^ S. Schweber: QED and the men who made it: Dyson, Schwinger, Feynman and Tomonaga, Princeton University Press 1994, ISBN 0691033277
10. ^ S. Schweber: The sources of Schwinger's Green's functions , PNAS vol. 102 no. 22 7783-7788