Dissipation via particle production in scalar field theories

Abstract

We study the nonequilibrium evolution of the expectation value of a scalar field in the broken and unbroken symmetry cases. We find that the particles produced by parametric amplification give rise to dissipative behavior for this mode. However, a l?d type of term cannot account for the dissipational dynamics. We are able to show clearly that perturbation theory breaks down at late times, so that dissipation in field theories can only be understood nonperturbatively. When Goldstone bosons are present we find infrared divergences that require a nonperturbative resummation to describe the long-time dynamics. We use the Hartree factorization and the large N approximation to the O(N) linear a model to numerically as well as analytically understand the long-time behavior of the zero mode as well as that of the produced particles. The O(N) model case is extremely interesting since, in the spontaneously broken case, the radial mode dissipates all of its energy into production of longwavelength Goldstone modes. The minima of the effective action (determined by the final value of the expectation value of the scalar field) depend on the initial conditions.

Effective field theory in time-dependent settings

“…As long as 1 2 λφ 2 ≪ m 2 , we can do so consistently; when this condition is not satisfied, we must instead define an effective, time dependent mass, m 2 eff (t) = m 2 + 1 2 λφ 2 (t). The behavior of the field in this regime can then be found numerically [12].…”

“…It is therefore helpful to have tools or tricks that can simplify the analysis whenever possible. One such tool is the tadpole method [12,13], which uses the equation of motion for a classical background field to follow the quantum loop corrections of a theory.…”

Renormalisability of the 2PI-Hartree approximation of multicomponent scalar models in the broken symmetry phase

“…At tree (classical) level this background results in different multiplet structures in the two sectors, but solving (81) iteratively one can show that the emerging exact mass spectra will have eventually the same structure in both sectors due to the coupling realised by the tensor H. To be specific, when v 3 = 0, v 8 = 0 one has 3 degenerate doublets in the "planes" [1,2], [4,5] and [6,7] and one coupled set with unequal eigenvalues in the [3,8] "plane". These "planes" correspond to the pairs of fields…”

“…In quantum field theory it corresponds to the momentum independent two-loop truncation of the two-particle irreducible effective action. It is used extensively both in equilibrium [2,3,4] and out-of-equilibrium [5,6,7,8] non-perturbative investigations of phase transition phenomena. Its non-perturbative renormalisability was demonstrated as particular case of the general proof of renormalisability of the physical quantities computed in various 2PI approximations [9,1,10].…”

Recent progress in inflationary cosmology

“…This may happen if the Hubble constant induced by the scalar eld is much greater than the curvature of the potential V ( ): m M P > M : (2) This decay can be easily suppressed if one introduces a small interaction g 2 2 2 between these two elds, which stabilizes the state with = 0 at large . Another possibility i s t o a d d a nonminimal interaction with gravity of the form 2 R 2 , which makes in ation impossible for > M P 8 .…”