Equal-time reduction of the Bethe–Salpeter formalism for a two-fermion system

The method of equal-time reduction proposed by the author [10, 11] for a system of two scalar particles is generalized to a system of two fermions. A self-consistent procedure for equal-time reduction is constructed both in terms of Bethe–Salpeter wave functions and in terms of Green's functions of the two-fermion system. Three-dimensional dynamical equations are obtained for the equal-time wave functions and the two-time Green's functions of the system of two fermions, and it is shown that the Schrödinger structure of the obtained equations is a consequence of the causal structure of local quantum field theory.