[en] Phase space representations (PSRs) are introduced in quantum field theory along the line of the Dirac representation theory. Nonoperator and left and right operator representatives for operators (observables) are defined. A Liouville equation (functional derivative one) for a phase space density in the Schroedinger picture and for the nonoperator representatives of operators in the Heisenberg picture is adopted as an equation of motion. Laws of quantum evolution for the operator representatives are also given in terms of a Liouvillian. It is shown that in PSR of the Wigner type evolution of fields and the phase space density is manifestly causal, i. e., is expressed only in terms of δsub(ret)-''functions''. In this PSR linear theories (Lagrangian at most bilinear) coincide with their classical analogs. In general case a some formal transition to h=0 leads to classical field theory equations and quantities, corresponding to quantum ones in the Schroedinger, Heisenberg and interaction pictures. The Hamilton and Lagrange equations of classical field theory appear naturally as ones for characteristics of a classical Liouville equation