A window on infrared QCD with small expansion parameters.

Lattice simulations of the QCD correlation functions in the Landau gauge have established two remarkable facts. First, the coupling constant in the gauge sector-defined, e.g., in the Taylor scheme-remains finite and moderate at all scales, suggesting that some kind of perturbative description should be valid down to infrared momenta. Second, the gluon propagator reaches a finite nonzero value at vanishing momentum, corresponding to a gluon screening mass. We review recent studies which aim at describing the long-distance properties of Landau gauge QCD by means of the perturbative Curci-Ferrari model. The latter is the simplest deformation of the Faddeev-Popov Lagrangian in the Landau gauge that includes a gluon screening mass at tree-level. There are, by now, strong evidences that this approach successfully describes many aspects of the infrared QCD dynamics. In particular, several correlation functions were computed at one- and two-loop orders and compared withab-initiolattice simulations. The typical error is of the order of ten percent for a one-loop calculation and drops to few percents at two loops. We review such calculations in the quenched approximation as well as in the presence of dynamical quarks. In the latter case, the spontaneous breaking of the chiral symmetry requires to go beyond a coupling expansion but can still be described in a controlled approximation scheme in terms of small parameters. We also review applications of the approach to nonzero temperature and chemical potential.

Effective potential for quantum scalar fields in a de Sitter geometry.

We study the quantum theory of an O(N) scalar field on de Sitter geometry at leading order in a nonperturbative 1/N expansion. This resums the infinite series of so-called superdaisy loop diagrams. We obtain the de Sitter symmetric solutions of the corresponding, properly renormalized, dynamical field equations and compute the complete effective potential. Because of its self-interactions, the field acquires a strictly positive square mass which screens potential infrared divergences. Moreover, strongly enhanced ultralong-wavelength fluctuations prevent the existence of a spontaneously broken symmetry state in any dimension.

Decoherence and thermalization of a pure quantum state in quantum field theory.

We study the real-time evolution of a self-interacting O(N) scalar field initially prepared in a pure, coherent quantum state. We present a complete solution of the nonequilibrium quantum dynamics from a 1/N expansion of the two-particle-irreducible effective action at next-to-leading order, which includes scattering and memory effects. We demonstrate that, restricting one's attention (or ability to measure) to a subset of the infinite hierarchy of correlation functions, one observes an effective loss of purity or coherence and, on longer time scales, thermalization. We point out that the physics of decoherence is well described by classical statistical field theory.

Parametric resonance in quantum field theory.

We present the first study of parametric resonance in quantum field theory from a complete next-to-leading order calculation in a 1/N expansion of the two-particle irreducible effective action, which includes scattering and memory effects. We present a complete numerical solution for an O(N)-symmetric scalar theory and provide an approximate analytic description of the nonlinear dynamics in the entire amplification range. We find that the classical resonant amplification at early times is followed by a collective amplification regime with explosive particle production in a broad momentum range, which is not accessible in a leading-order calculation.