Pair creation in Feshbach-Villars formalism with two components
- 61 Downloads
We have studied the behavior of the Feshbach-Villars equation (FV0) in comparison with the Klein-Gordon one (KG) in the problem of particle pair creation from the vacuum in an external electromagnetic field, considering two approaches: the Schwinger effective action method and the Bogoliubov transformation technique. In the first approach the vacuum to vacuum transition amplitude is calculated treating the FV0 field like a bosonic field. For the second approach, that uses canonical quantization, it is shown that the relative fields and their conjugate moments obey a commutation relation and not anticommutation one. The pair creation probability and the probability that the vacuum remains a vacuum calculated from the FV0 equation are, consequently, the same as those obtained from the KG one.
KeywordsElectromagnetic Field Transition Amplitude Commutation Relation Effective Action Particle Acceleration
Unable to display preview. Download preview PDF.
- 1.F. Gross, Relativistic quantum mechanics and field theory (Wiley-Interscience, New York 1993)Google Scholar
- 3.J.D. Bjorken, S.D. Drell, Relativistic quantum fields (McGraw Hill, New York 1965)Google Scholar
- 4.T. Boudjedaa, L. Chetouani, M. Merad, Il Nuovo Cimento 11, 1261 (1999); Chin. J. Phys. 6, 1020 (2000), Turk. J. Phys. 25, (2001)Google Scholar
- 10.B.R. Holstein, Am. J. Phys. 67, (Vol. 6) 499 (1998)Google Scholar
- 11.E.S. Fradkin, D.M. Gitman, S.M. Shvartsman, Quantum electrodynamics with unstable vacuum (Springer-Verlag, Berlin 1991)Google Scholar
- 12.A.I. Nikishov, hep-th/0111137Google Scholar
- 13.A.I. Nikishov, hep-th/0202024Google Scholar
- 14.S.P. Gavrilov, D.M. Gitman, hep-th/9603152 v1Google Scholar
- 17.I.S. Gradshteyn, I.M. Ryzhik, Table of integrals, series, and products (Academic Press, New York 1979)Google Scholar