Nonequilibrium dynamics: Preheating in the SU(2) Higgs model

Abstract

The term ''preheating'' has been introduced recently to denote the process in which energy is transferred from a classical inflaton field into fluctuating field ͑particle͒ degrees of freedom without generating yet a real thermal ensemble. The models considered up to now include, in addition to the inflaton field, scalar or fermionic fluctuations. On the other hand, the typical ingredient of an inflationary scenario is a non-Abelian spontaneously broken gauge theory. So the formalism should also be developed to include gauge field fluctuations excited by the inflaton or Higgs field. We have chosen here, as the simplest non-Abelian example, the SU͑2͒ Higgs model. We consider the model at temperature zero. From the technical point of view we generalize an analytical and numerical renormalized formalism developed by us recently to coupled channnel systems. We use the 't Hooft-Feynman gauge and dimensional regularization. We present some numerical results but reserve a more exhaustive discussion of solutions within the parameter space of two couplings and the initial value of the Higgs field to a future publication. ͓S0556-2821͑97͒00412-8͔

Gauge fields out of equilibrium: A gauge invariant formulation and the Coulomb gauge

“…We show how a proper renormalization can be implemented. Therefore, we use a scheme which was developed by us for the φ 4 theory [26] and extended to fermionic and gauge systems [22,27]. Furthermore, we show how the gauge invariant approach and the Coulomb gauge are related to each other.…”

“…In [22] we have presented the theoretical framework and its numerical implementation for the SU(2) Higgs model in the 't Hooft-Feynman background gauge. Obviously, the question of gauge dependence and independence has to be explored.…”

Choice of initial states in nonequilibrium dynamics

“…Nonequilibrium dynamics in quantum field theory has become, during the last years, a very active field of research in particle physics [1][2][3][4][5][6], in cosmology [7][8][9][10][11][12][13][14][15][16][17][18][19][20] , and in solid state physics [21]. The outline of typical computational experiments is as follows: a quantum field ψ(x, t) is driven by a classical field degree of freedom (Higgs, inflaton, condensate) φ(t) which takes an initial value away from a local or global minimum of the classical or effective action; the time development is then studied including the back reaction of the quantum field in one-loop, Hartree or large-N approximations.…”

Dynamics of coupled bosonic systems with applications to preheating

“…An alternative method has been developed [16,17,21] which relies on a formal perturbative expansion in the effective masses and time derivatives of the masses of the fields. As such, it results in a series expansion of the mode functions in powers of m/ω andṁ/ω 2 , etc.…”

“…In contrast to the WKB ansatz this method can be extended for coupled system, which was demonstrated in Ref. [17]. This procedure will be used also in this paper.…”