Particle production in quantum transport theories

The particle production in the intermediate-energy heavy-ion collisions is discussed in the framework of the nonequilibrium Green{close_quote}s functions formalism. The evolution equations of the Green{close_quote}s functions for fermions allows for the discussion of the off-shell fermion propagator and of the large momentum component in the initial state. For the case of a homogeneous system numerical calculations of the meson production rate are performed and compared with the semiclassical production rate. {copyright} {ital 1997} {ital The American Physical Society}