Studies on a phase transition in a scalar quantum field theory

This work deals with the dynamical instability of the vacuum in the (phi)2sigma scalar quantum field theory. This instability, which is related to the occurrence of a zero-mass phi-phi bound state, is most easily investigated in terms of the properties of the Schwinger-Dyson equation describing the self-energy corrections to the phi propagator. The main results of the work are: i) the functional formalism provides a coherent treatment of the problem in terms of the effective potential, the Schwinger-Dyson equation, and the Bethe-Salpeter equation; ii) there are two analytically related solutions to the nonlinear Schwinger-Dyson equation; iii) the important role of the zero-mass bound state Bethe-Salpeter equation - the particular value of the coupling constant at which the bound state occurs is the critical value of the coupling constant at which the phase transition takes place; and iv) the numerical solution of the dressed Bethe-Salpeter equation in the ladder approximation. At large values of the coupling constant the effect of self-energy corrections is significant