Creation and scattering of particles by a nonstationary electromagnetic field in the canonical formalism

A study is made of the creation and scattering of particles by a nonstationary electromagnetic field of arbitrary form. Bogolyubov's method of canonical transformations is used to obtain exact expressions for the number density of the fermion and boson pairs created by the external field and also for the amplitudes of transition from an arbitrary initial to an arbitrary final state. The explicit connection between the $\text{in}$- and $\text{out}$-vacuum states is found. In the framework of the proposed formalism, a proof is given in the general case of Feynman's assertion that, with allowance for particle creation by a field and the connection between spin and statistics, the total probability of scattering is equal to unity.