QUANTUM-FIELD THEORY AT FINITE-ENERGY

We give a general formulation of statistical quantum field theory at finite energy in the functional integral approach using the microcanonical distribution. Definitions of thermodynamical quantities and the effective potential are given. The Feynman rules for the real scalar field with phi4 interaction and some computations of physically interesting quantities are presented. We discuss how a structure which is the same as the statistical bootstrap comes into the theory in a natural way. The entropy in phi4 theory is calculated perturbatively up to two loops. The behaviour of symmetry at finite energy is investigated using the effective action and symmetry restoration at high energy is shown in a theory which has spontaneous symmetry breaking at zero energy. A detailed discussion is given using phi4 theory and the results in the model where the scalar boson is coupled to fermions are also presented. Finally, applications and the perspectives of the formalism are discussed.