Pressure of hot<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="italic">g</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">φ</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>theory at order<mml:math xmlns:mml="http://w

Parwani, Rajesh R.; Singh, Harvendra

doi:10.1103/physrevd.51.4518

Cited by 60 publications

(81 citation statements)

References 12 publications

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“…This difference of behavior of perturbation theory at zero and finite temperature can be understood from the fact that, at finite temperature, the expansion parameter involves both the coupling and the magnitude of thermal fluctuations (for a recent review, see [2]; see also [3]). In that respect, the problem is not specific to QCD: Similar poor convergence behavior appears also in the simpler scalar field theory [4], and has also been observed in the case of large-N φ 4 theory [5]. Similar observations can be made also in the case of QED [6].…”

Section: Introductionsupporting

confidence: 59%

Calculation of the pressure of a hot scalar theory within the Non-Perturbative Renormalization Group

2011

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We apply to the calculation of the pressure of a hot scalar field theory a method that has been recently developed to solve the Non-Perturbative Renormalization Group. This method yields an accurate determination of the momentum dependence of n-point functions over the entire momentum range, from the low momentum, possibly critical, region up to the perturbative, high momentum region. It has therefore the potential to account well for the contributions of modes of all wavelengths to the thermodynamical functions, as well as for the effects of the mixing of quasiparticles with multi-particle states. We compare the thermodynamical functions obtained with this method to those of the so-called Local Potential Approximation, and we find extremely small corrections. This result points to the robustness of the quasiparticle picture in this system. It also demonstrates the stability of the overall approximation scheme, and this up to the largest values of the coupling constant that can be used in a scalar theory in 3+1 dimensions. This is in sharp contrast to perturbation theory which shows no sign of convergence, up to the highest orders that have been recently calculated.

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Section: Introductionsupporting

confidence: 59%

Calculation of the pressure of a hot scalar theory within the Non-Perturbative Renormalization Group

2011

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“…(5.18)), the resummation then reduces to including m 2 D in the electric propagator. By using this technique, the free energy has been computed up to order g 5 for massless scalar φ 4 theory [179,180], Abelian gauge theories [181,182], and QCD [178,183]. These results have been reobtained by using the dimensionally-reduced effective theory in Refs.…”

Section: Some Applications Of Htl-resummed Perturbation Theorymentioning

confidence: 99%

“…3. By taking x 0 and y 0 real, with x 0 later (respectively, earlier) than y 0 , we get: 180) or, after a Wigner transform,…”

Section: Damping Rates From Kinetic Equationsmentioning

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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“…At high temperature, the perturbative expansion of the thermodynamic potential is known to 5th order in the coupling for the φ 4 theory [1], [2], for QED [3], and for QCD [4], [5]. However, for physically relevant questions the applicability of these results is limited; they are meaningful only when the coupling is so weak that the thermodynamic potential is very close to its free limit.…”

Section: Introductionmentioning

confidence: 99%