Feynman-Stückelberg interpretation

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The Feynman - Stückelberg interpretation is an important tool when applying the Dirac equation . Above all, it explains the question of the interpretation of the solutions or states with negative energies. These were originally interpreted by Dirac himself with the help of the so-called Dirac lake , which from a physical point of view includes the disadvantage of an infinitely high mass without gravitational effect. Due to the interpretation of the states with negative energy by Feynman and Stückelberg, Lake Dirac is not considered real today.

The Feynman-Stückelberg interpretation was developed in order to be able to correctly describe the behavior of the corresponding antiparticles , i.e. the positrons , in addition to the calculation of the relativistic dynamics of electrons . With their help, elementary processes of quantum electrodynamics , such as the cross-section for pair generation or pair annihilation of electrons and positrons, can be calculated comparatively easily with the aid of Feynman diagrams .

A state with negative energy is interpreted as a state with positive energy, an inverse charge, a mirrored space and reversed time direction. The wave function of an electron with negative energy corresponds to the wave function of a positron moving backwards in time in a mirrored space. The reverse assignment between positron and electron is also permitted.

The so-called CPT symmetry also exists between electron and positron . This transformation is composed of the three individual transformations, in which the charge (engl. C harge), parity ( P arity) and time direction ( T ime) can be reversed, respectively, together. In contrast to other fundamental equations, the Dirac equation with the coupling to the electromagnetic field also has the individual symmetries and their combinations, such as CP.

literature

  • Cours de physique stueckelberg (French)
  • Richard P. Feynman : Quantum Electrodynamics - A Lecture Notes . With an appendix by Harald Fritzsch . 4th revised edition. Oldenbourg, Munich et al. 1997, ISBN 3-486-24337-3 .
  • Walter Greiner : Theoretical Physics . Volume 6: Relativistic Quantum Mechanics. Wave equations . 2nd revised and expanded edition. Deutsch, Thun et al. 1987, ISBN 3-8171-1022-7
  • James D. Bjorken , Sidney D. Drell : Relativistic quantum mechanics (= BI university pocket books . Vol. 98 / 98a). Unchanged reprint. Bibliographisches Institut, Mannheim et al. 1990, ISBN 3-411-00098-8 (English original edition: Relativistic Quantum Mechanics . McGraw Hill, New York NY et al. 1964)
  • James Bjorken, Sidney Drell: Relativistic quantum field theory (= BI university paperbacks. Vol. 101). Unchanged reprint. Bibliographisches Institut, Mannheim et al. 1993, ISBN 3-411-00101-1 (English original edition: Relativistic Quantum Fields . McGraw Hill, New York NY et al. 1965)
  • Stephen Hawking : A Brief History of Time (= rororo. Rororo non-fiction. Rororo Science 60555). New edition, 456th - 475th thousand. Rowohlt, Reinbek bei Hamburg 1998, ISBN 3-499-60555-4 , pp. 185 ff.