Pair creation of spin-1/2 particles in Feshbach–Villars formalism

The Feshbach–Villars equation (FV 1/2 ) is studied by comparing it with the Dirac equation and by examining its behaviour in the creation process of pairs of particles from vacuum while being perturbed by an external field using two approaches: (i) the effective action method of Schwinger and (ii) the Bogoliubov transformation. In the first approach, the transition vacuum–vacuum amplitude is determined by treating the FV 1/2 field as a fermionic field. In the second approach, the anticommutation relations are used contrary to the case of spin 0, in order to obtain meaningful probabilities. The two approaches show that the expressions of pair creation probability as well as those relating to the vacuum remaining vacuum are exactly similar to those obtained by either FV 1/2 or Dirac equations.