Aspects of the functional renormalisation group

Pawlowski, Jan M.

doi:10.1016/j.aop.2007.01.007

Cited by 903 publications

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“…(6) is nothing but an infinitesimal closed time loop at τ , which is by itself finite and requires no further renormalisation. However, in particular in higher dimensions additional regulators in the spatial or momentum domains may be advantageous for facilitating renormalisation and thus the practical application of the approach, see [13,14,16]. We also emphasise that the evolution equation (6), even though close in spirit and construction to standard functional RG equations, is conceptually different.…”

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confidence: 99%

“…It entails a physical time evolution as opposed to integrating out degrees of freedom. Nevertheless, more general regulators R τ may be advantageous in other cases [16], e.g., when a cutoff is set in the relative time (t−t ′ -) direction, see Fig. 2.…”

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confidence: 99%

“…It is analogous to functional flow equations used extensively with regulators in momentum and/or frequency space to describe strongly correlated systems near equilibrium [13,14,15,16]. Its homogenous part relates to standard τ -dependent renormalisation [16], and has been studied eg. in [20,21].…”

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confidence: 99%

“…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-equilibrium evolutions. Moreover, the hierarchy of equations is technically very close to 2PI and Dyson-Schwinger type evolutions, see [16], as well as to evolution equations for the effective action …”

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confidence: 99%

“…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-equilibrium evolutions.…”

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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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Section: Fig 2: (Color Online)mentioning

confidence: 99%

Section: Fig 2: (Color Online)mentioning

confidence: 99%

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

2008

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Functional renormalization group approach to the BCS‐BEC crossover

Diehl¹,

et al. 2010

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The phase transition to superfluidity and the BCS-BEC crossover for an ultracold gas of fermionic atoms is discussed within a functional renormalization group approach. Non-perturbative flow equations, based on an exact renormalization group equation, describe the scale dependence of the flowing or average action. They interpolate continuously from the microphysics at atomic or molecular distance scales to the macroscopic physics at much larger length scales, as given by the interparticle distance, the correlation length, or the size of the experimental probe. We discuss the phase diagram as a function of the scattering length and the temperature and compute the gap, the correlation length and the scattering length for molecules. Close to the critical temperature, we find the expected universal behavior. Our approach allows for a description of the few-body physics (scattering and molecular binding) and the many-body physics within the same formalism.

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Quantum Spacetime and the Renormalization Group: Progress and Visions

Pereira

2020

Progress and Visions in Quantum Theory in View of Gravity

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Aspects of the functional renormalisation group

Cited by 903 publications

References 185 publications

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

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

Functional renormalization group approach to the BCS‐BEC crossover

Quantum Spacetime and the Renormalization Group: Progress and Visions

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