Consistent quantization of systems with positive and negative energy states

The Stueckelberg-Feynman (SF) treatment, where positive energy antiparticles are described as negative energy particles going backward in time, lies on the basis of particle physics, but it was inconsistent with quantum field theory, since led to a negative norm for negative energy states. In the paper a new consistent method of canonical quantization in SF treatment is presented, where norms of all states is positive, since changing the direction of time integration in the action function changes the sign of Lagrangian of antiparticles and momentum. Minimal Lagrangians for complex canonical variables do not lead to the zero-point energy, which partially solves the cosmological constant problem. Causal propagators and amplitudes appear as symmetric chronological products of field operators, which slightly modifies diagram technique. Modified microcausality conditions and proof of spin and statistics theorem are presented, applications to particle physics and condensed media are discussed.