Approximately self-consistent resummations for the thermodynamics of the quark-gluon plasma: Entropy and density

Blaizot, Jean‐Paul; Iancu, Edmond; Rebhan, Anton

doi:10.1103/physrevd.63.065003

Cited by 309 publications

(337 citation statements)

References 62 publications

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“…In order to develop these methods for strongly interacting systems, we need to take account of the constraints in the theory, requiring a Luttinger Ward approach appropriate to gauge theories. In this respect, our efforts to apply the Luttinger Ward approach to the Kondo lattice closely parallel recent efforts to extend the Luttinger Ward approach to quark-gluon plasmas [21].…”

Section: Luttinger Ward Expression For the Kondo Latticementioning

confidence: 78%

“…• This approach is general, and can, for example be applied to the interacting electron gas, and various interacting plasmas, such as the quark gluon plasma [21]. By treating the interaction line as an independent particle (photon), the leading order approximation generates a generalized RPA-Eliashberg scheme for the self-consistent interaction and electron self-energies.…”

Section: Entropy Formulamentioning

confidence: 99%

“…Our approach is based on the use of slave particles, such as a Schwinger boson description for the local moments in a Kondo lattice. We begin with a generalization of the Luttinger Ward Free energy functional, appropriate for systems of interacting bosons and fermions [20,21] which can be compactly written as where the use of the supertrace as the measure for functional derivatives avoids the need to introduce a relative minus sign between Fermi and Bose parts of this expression. Diagrammatically, the functional derivative of Y with respect to G corresponds to "cutting" one of its internal lines.…”

Section: Introductionmentioning

confidence: 99%

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Sum rules and Ward identities in the Kondo lattice

2005

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We derive a generalized Luttinger-Ward expression for the Free energy of a many body system involving a constrained Hilbert space. In the large N limit, we are able to explicitly write the entropy as a functional of the Green's functions. Using this method we obtain a Luttinger sum rule for the Kondo lattice. One of the fascinating aspects of the sum rule, is that it contains two components, one describing the heavy electron Fermi surface, the other, a sea of oppositely charged, spinless fermions. In the heavy electron state, this sea of spinless fermions is completely filled and the electron Fermi surface expands by one electron per unit cell to compensate the positively charged background, forming a "large" Fermi surface. Arbitrarily weak magnetism causes the spinless Fermi sea to annihilate with part of the Fermi sea of the conduction electrons, leading to a small Fermi surface. Our results thus enable us to show that the Fermi surface volume contracts from a large, to a small volume at a quantum critical point. However, the sum rules also permit the possible formation of a new phase, sandwiched between the antiferromagnet and the heavy electron phase, where the charged spinless fermions develop a true Fermi surface.

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Section: Luttinger Ward Expression For the Kondo Latticementioning

confidence: 78%

Section: Entropy Formulamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Sum rules and Ward identities in the Kondo lattice

2005

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“…Furthermore, the QPM expression for the shear viscosity from Eq. (1) [76] and entropy densitys from [117]. The band was obtained by varying the renormalization point μ in the QCD running coupling g(μ) in the range πT μ 4πT .…”

Section: The Shear Viscositymentioning

confidence: 99%

Shear and bulk viscosities of the gluon plasma in a quasiparticle description

2011

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Shear and bulk viscosities of deconfined gluonic matter are investigated within an effective kinetic theory by describing the strongly interacting medium phenomenologically in terms of quasiparticle excitations with medium-dependent self-energies. We show that the resulting transport coefficients reproduce the parametric dependencies on temperature and coupling obtained in perturbative QCD at large temperatures and small running coupling. The extrapolation into the nonperturbative regime results in a decreasing specific shear viscosity with decreasing temperature, exhibiting a minimum in the vicinity of the deconfinement transition, while the specific bulk viscosity is sizable in this region, falling off rapidly with increasing temperature. The temperature dependence of specific shear and bulk viscosities found within this quasiparticle description of the pure gluon plasma is in agreement with available lattice QCD results.

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“…The possibility to identify and perform such resummations offers a chance to extrapolate weak coupling results down to temperature where the coupling is not really small (recall that the dependence of the coupling on the temperature is only logarithmic, and it is only for T ≫ T c , where T c is the deconfinement temperature, that the coupling is truly small). Recent works indicate that this strategy may indeed be successful [30,31,32].…”

Section: Introductionmentioning

confidence: 99%

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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Approximately self-consistent resummations for the thermodynamics of the quark-gluon plasma: Entropy and density

Cited by 309 publications

References 62 publications

Sum rules and Ward identities in the Kondo lattice

Sum rules and Ward identities in the Kondo lattice

Shear and bulk viscosities of the gluon plasma in a quasiparticle description

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

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