Renormalization out of equilibrium in a superrenormalizable theory

Renormalization in momentum dependent resummations

At finite temperature and in non-equilibrium environments we have to resum perturbation theory to avoid infrared divergences. Since resummation shuffles the perturbative orders, renormalizability is a nontrivial issue. In this paper we demonstrate that one can modify any type of resummations -- even if it is momentum dependent, or it resums higher point functions -- in a way that it is renormalizable with the usual zero temperature counterterms. To achieve this goal we reformulate resummation in form of a renormalization scheme. We apply this technique to perform a 2PI resummation in the six d…

远离平衡态中的重整化群

Renormalization Group in far-from-equilibrium states

本文研究远离平衡态中的重整化群流，发现正γ降低算符维度，使边际相互作用变为相关，并构建了ε展开与红外不动点，揭示临界平衡标度对应态沿RG流动态调整至边际相互作用。

Non-Fermi Liquid Aspects of Cold and Dense QED and QCD: Equilibrium and Non-Equilibrium

Infrared divergences from the exchange of dynamically screened magnetic gluons (photons) lead to the breakdown of the Fermi liquid description of the {\em normal} state of cold and dense QCD and QED. We implement a resummation of these divergences via the renormalization group to obtain the spectral density, dispersion relation, widths and wave function renormalization of single quasiparticles near the Fermi surface. We find that all feature scaling with anomalous dimensions: $ω_p({k}) \propto |k-k_F|^{\frac{1}{1-2λ}} ~ ; ~ Γ(k) \propto |k-k_F|^{\frac{1}{1-2λ}} ~;~ Z_p({k}) \propto |k-k_F|^{\f…

Renormalization and resummation in field theories

Using resummation in perturbation theories at finite temperature or in non-equilibrium is unavoidable to obtain consistent results. Resummation, however, is often in conflict with renormalization. In this talk we give two possible solutions to problems of this type in static resummation. One is the use of auxiliary finite temperature UV divergent counterterms. The other is to use a renormalization scheme fitted to the environment. We also suggest a way how one could proceed in case of dynamic resummations.

Stochastic Quantization of Autonomous Phi**4

The non-perturbative autonomous renormalization of the scalar $Φ^4$-model is applied in the framework of stochastic quantization. I show that this requires a selective, momentum-dependent renormalization of the Onsager coefficient $λ$, a direct consequence of the characteristic wavefunction renormalization applied. As a result, I obtain a Langevin equation for the renormalized constant mode of the field, which is solved numerically. It is demonstrated for temperature zero that, starting from specified initial conditions, the system relaxes to its equilibrium state, the symmetry-breaking vacuum…

Nonperturbative renormalization of Phi-derivable approximations in theories with fermions

We show how to renormalize Phi-derivable approximations in a theory with a fermionic field coupled to a self-interacting scalar field through a Yukawa interaction. The nonperturbative renormalization concerns the self-interaction coupling of the scalar field which is renormalized via a set of nested Bethe-Salpeter equations for the scalar and fermionic four-point functions. We use this information to construct explicit finite equations of motion in the symmetric phase. We work in the context of equilibrium quantum field theory and show that the renormalization can be carried out without introd…

Non-Equilibrium Large N Yukawa Dynamics: marching through the Landau pole

The non-equilibrium dynamics of a Yukawa theory with N fermions coupled to a scalar field is studied in the large N limit with the goal of comparing the dynamics predicted from the renormalization group improved effective potential to that obtained including the fermionic backreaction. The effective potential is of the Coleman-Weinberg type. Its renormalization group improvement is unbounded from below and features a Landau pole. When viewed self-consistently, the initial time singularity does not arise. The different regimes of the dynamics of the fully renormalized theory are studied both an…

Quantum scalar fields in de Sitter space from the nonperturbative renormalization group

We investigate scalar field theories in de Sitter space by means of nonperturbative renormalization group techniques. We compute the functional flow equation for the effective potential of O(N) theories in the local potential approximation and we study the onset of curvature-induced effects as quantum fluctuations are progressively integrated out from subhorizon to superhorizon scales. This results in a dimensional reduction of the original action to an effective zero-dimensional Euclidean theory. We show that the latter is equivalent both to the late-time equilibrium state of the stochastic a…

Gauge Fields Out-Of-Equilibrium: A Gauge Invariant Formulation and the Coulomb Gauge

We study the abelian Higgs model out-of-equilibrium in two different approaches, a gauge invariant formulation, proposed by Boyanovsky et al. \cite{Boyanovsky:1996dc} and in the Coulomb gauge. We show that both approaches become equivalent in a consistent one loop approximation. Furthermore, we carry out a proper renormalization for the model in order to prepare the equations for a numerical implementation. The additional degrees of freedom, which arise in gauge theories, influence the behavior of the system dramatically. A comparison with results in the 't Hooft-Feynman background gauge found…

Fluid dynamics of out of equilibrium boost invariant plasmas

We establish a set of equations for moments of the distribution function. In the relaxation time approximations, these moments obey a coupled set of equations that can be truncated order-by-order. Solving the equations of moments, we are able to identify an attractor solution that controls a transition from a free streaming fixed point to a hydrodynamic fixed point. In particular, this attractor solution provides a renormalization of the effective value of the shear viscosity to entropy density ratio, $η/s$, taking into account off-equilibrium effects.