BOSON CONDENSATIONS IN REAL-TIME THERMAL QUANTUM-FIELD THEORY

Solving the transport equation or considering the entropy law, we find that the equilibrium number density can be generalized to account for Bose-Einstein condensations of gapless energy bosons in the real time formalism of finite temperature quantum field theory, without recours e to broken phase symmetry. It is shown that in equilibrium situations there is an additional term in the number density at zero momentum wh ich can remain finite even at zero temperature.