The effects of bosonic trilinear interactions are investigated in the process of resonant particle production. We study a generic model of three fields with trilinear couplings. In this model a scalar field Φ can excite a heavy bosonic field χ which then decays into a light bosonic field σ. We study the consequences of dissipation and stochastic noise terms in the field equations of motion that result from a calculation in nonequlibrium quantum field theory and determine the effects of these terms for the phenomenon of parametric resonance, which can occur e.g. during preheating after inflation.

We consider the modification of the Cahn-Hilliard equation when a time delay process through a memory function is taken into account. We then study the process of spinodal decomposition in fast phase transitions associated with a conserved order parameter. The introduced memory effect plays an important role to obtain a finite group velocity. Then, we discuss the constraint for the parameters to satisfy causality. The memory effect is seen to affect the dynamics of phase transition at short times and have the effect of delaying, in a significant way, the process of rapid growth of the order parameter that follows a quench into the spinodal region.

We use the linear delta expansion, or optimized perturbation theory, to evaluate the effective potential for the two dimensional Gross-Neveu model at finite temperature and density obtaining analytical equations for the critical temperature, chemical potential and fermionic mass which include finite N corrections. Our results seem to improve over the traditional large-N predictions.

Topological excitations are believed to play an important role in different areas of physics. For example, one case of topical interest is the use of dual models of quantum cromodynamics to understand properties of the vacuum and confinement through the condensation of magnetic monopoles and vortices. Other applications are related to the role of these topological excitations, nonhomogeneous solutions of the field equations, in phase transitions associated to spontaneous symmetry breaking in gauge theories, whose study is of importance, for instance, in phase transitions in the early universe. Here we show a derivation of a model dual to the scalar Abelian Higgs model where its topological excitations, namely vortex-strings, become manifest and can be treated in a quantum field theory way. The derivation of the nontrivial contribution of these vacuum excitations to phase transitions and its analogy with superconductivity is then made possible and they are studied here.