Dynamical renormalization group resummation of finite temperature infrared divergences

Boyanovsky, D.; Vega, H. J. de; Holman, R.; Simionato, M.

doi:10.1103/physrevd.60.065003

Cited by 77 publications

(225 citation statements)

References 80 publications

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“…Another approach leading to a similar exponentiation of the one-loop result is the so-called "dynamical renormalization group" developed in Refs. [99,69,132]. …”

Section: Discussionmentioning

confidence: 99%

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The quark–gluon plasma: collective dynamics and hard thermal loops

Blaizot¹,

Iancu²

2002

Physics Reports

515

714

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We present a unified description of the high temperature phase of QCD, the so-called quark-gluon plasma, in a regime where the effective gauge coupling g is sufficiently small to allow for weak coupling calculations. The main focuss is the construction of the effective theory for the collective excitations which develop at a typical scale gT , which is well separated from the typical energy of single particle excitations which is the temperature T . We show that the short wavelength thermal fluctuations, i.e., the plasma particles, provide a source for long wavelength oscillations of average fields which carry the quantum numbers of the plasma constituents, the quarks and the gluons. To leading order in g, the plasma particles obey simple gauge-covariant kinetic equations, whose derivation from the general Dyson-Schwinger equations is outlined. By solving these equations, we effectively integrate out the hard degrees of freedom, and are left with an effective theory for the soft collective excitations. As a by-product, the "hard thermal loops" emerge naturally in a physically transparent framework. We show that the collective excitations can be described in terms of classical fields, and develop for these a Hamiltonian formalism. This can be used to estimate the effect of the soft thermal fluctuations on the correlation functions. The effect of collisions among the hard particles is also studied. In particular we discuss how the collisions affect the lifetimes of quasiparticle excitations in a regime where the mean free path is comparable with the range of the relevant interactions. Collisions play also a decisive role in the construction a Member of CNRS. E-mail: blaizot@spht.saclay.cea.fr b Member of CNRS. E-mail: iancu@spht.saclay.cea.fr c Laboratoire de la Direction des Sciences de la Matière du Commissariatà l'Energie Atomique of the effective theory for ultrasoft excitations, with momenta ∼ g 2 T , a topic which is briefly addressed at the end of this paper.

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“…Another approach leading to a similar exponentiation of the one-loop result is the so-called "dynamical renormalization group" developed in Refs. [99,69,132]. …”

Section: Discussionmentioning

confidence: 99%

“…A more complicated behaviour can occur whenever some of the aforementioned assumptions are not satisfied. In section 6, we shall encounter an example of such a non-trivial evolution in time [68,97,98,99].…”

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confidence: 99%

The quark–gluon plasma: collective dynamics and hard thermal loops

Blaizot¹,

Iancu²

2002

Physics Reports

515

714

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show abstract

“…Its homogenous part relates to standard τ -dependent renormalisation [16], and has been studied eg. in [20,21]. We close the derivation of the evolution equation with some remarks: Eq.…”

Section: Fig 2: (Color Online)mentioning

confidence: 99%

Towards far-from-equilibrium quantum field dynamics: A functional renormalisation-group approach

2008

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Dynamic equations for quantum fields far from equilibrium are derived by use of functional renormalisation group techniques. The obtained equations are non-perturbative and lead substantially beyond mean-field and quantum Boltzmann type approximations. The approach is based on a regularised version of the generating functional for correlation functions where times greater than a chosen cutoff time are suppressed. As a central result, a time evolution equation for the non-equilibrium effective action is derived, and the time evolution of the Green functions is computed within a vertex expansion. It is shown that this agrees with the dynamics derived from the 1/N -expansion of the two-particle irreducible effective action.PACS numbers: 03.75. Kk, 05.10.Cc, 05.70.Ln, Introduction. Far-from-equilibrium quantum field dynamics is one of the most challenging issues both in experimental and theoretical physics to date. Experiments exhibiting quantum statistical effects in the time evolution of many-body systems are extremely demanding. In particular, the preparation of ultracold atomic Bose and Fermi gases in various trapping environments allows to precisely study quantum many-body dynamics of strongly correlated systems, see, e.g., Refs.[1]. In recent years, the field has attracted researchers from a variety of disciplines, ranging from condensed-matter to highenergy particle physics and cosmology. Nonequilibrium field theory to date is dominated by semi-classical mean-field approaches which are in general only valid for weak interactions or large occupation numbers. For strongly correlated quantum systems methods are available predominantly for systems in one spatial dimension and include the Density Matrix Renormalisation Group methods, see e.g. [2], as well as techniques for exactly solvable models [3]. Non-perturbative approximations of the two-particle irreducible (2PI) effective action [4] have been intensively studied and applied to nonequilibrium dynamics [5,6,7,8,9,10,11] and are applicable also in more than one dimension. In field theory, they also provide a way to study strongly correlated fermions beyond mean-field and Boltzmann approximations [8]. Like these, the results presented here are expected to be of high relevance, e.g., for the description of ultracold degenerate Fermi gases close to the BEC-BCS crossover [12].In this paper we derive dynamic equations for quantum fields far from equilibrium. As a central result, we derive a new time evolution equation for the non-equilibrium effective action by use of functional renormalisation group (RG) techniques, cf. Refs. [13,14,15,16], as well as [17] for non-equilibrium applications. This exact and closed evolution equation allows for non-perturbative approximations that lead substantially beyond mean-field and quantum Boltzmann type approaches: it can be rewritten, in a closed form, as a hierarchy of dynamical equations for Green functions, and this hierarchy admits truncations that neither explicitly nor implicitly rely on small bare couplings or close-to...

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“…These papers should be useful to the reader who is unsatisfied with my presentation, or wants to extend it. During the last several years, [53,54,55,56,57,58,59] have extended and generalized this dynamical renormalization group method to compute the real time evolution of expectation values of quantum fields.…”

Section: Introductionmentioning

confidence: 99%

Dark matter clustering: A simple renormalization group approach

McDonald

2007

Phys. Rev. D

112

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I compute a renormalization group (RG) improvement to the standard beyond-linear-order Eulerian perturbation theory (PT) calculation of the power spectrum of large-scale density fluctuations in the Universe. At z = 0, for a power spectrum matching current observations, lowest order RGPT appears to be as accurate as one can test using existing numerical simulation-calibrated fitting formulas out to at least k ≃ 0.3 h Mpc −1 ; although inaccuracy is guaranteed at some level by approximations in the calculation (which can be improved in the future). In contrast, standard PT breaks down virtually as soon as beyond-linear corrections become non-negligible, on scales even larger than k = 0.1 h Mpc −1 . This extension in range of validity could substantially enhance the usefulness of PT for interpreting baryonic acoustic oscillation surveys aimed at probing dark energy, for example. I show that the predicted power spectrum converges at high k to a power law with index given by the fixed-point solution of the RG equation. I discuss many possible future directions for this line of work. The basic calculation of this paper should be easily understandable without any prior knowledge of RG methods, while a rich background of mathematical physics literature exists for the interested reader.PACS numbers: 98.65. Dx, 05.10.Cc, 95.35.+d, 98.80.Es

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Dynamical renormalization group resummation of finite temperature infrared divergences

Cited by 77 publications

References 80 publications

The quark–gluon plasma: collective dynamics and hard thermal loops

The quark–gluon plasma: collective dynamics and hard thermal loops

Towards far-from-equilibrium quantum field dynamics: A functional renormalisation-group approach

Dark matter clustering: A simple renormalization group approach

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