Pair creation in Feshbach-Villars formalism with two components
Département de Physique, Faculté de Sciences, Université Mentouri, Route Ain El-Bey, 25000, Constantine, Algérie
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.
© Springer-Verlag, 2005