Pressure in thermal scalar field theory to three-loop order

Frenkel, Jacob A.; Saa, Alberto; Taylor, John

doi:10.1103/physrevd.46.3670

Cited by 55 publications

(95 citation statements)

References 6 publications

(6 reference statements)

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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%

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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Section: Some Applications Of Htl-resummed Perturbation Theorymentioning

confidence: 99%

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

Blaizot¹,

Iancu²

2002

Physics Reports

515

714

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“…If these g E,i 's are expanded in powers of g, then Eq. (8) yields the formula for F that was originally obtained perturbatively by including the ring-diagram resummation [5,7]. It is a check of consistency of the effective field approach to show that the total expression for F is independent of the factorization scale Λ.…”

Section: Separation Of Long and Short Distance Regimesmentioning

confidence: 99%

“…It is crucial to keep in mind the origin of the various terms: The terms ∼ a 3/2 and ∼ a 5/2 come exclusively from the resummation of the ring diagrams that is necessary to avoid infrared divergences [5,7]. This resummation procedure also yields part of the coefficient C 4 of the ∼ a 2 term.…”

Section: Separation Of Long and Short Distance Regimesmentioning

confidence: 99%

“…They have been calculated recently [5,6,7,8] up to ∼ g 5 , i.e., three loops plus all the ring diagrams summed up. The generic structure of the resulting expressions is…”

Section: Separation Of Long and Short Distance Regimesmentioning

confidence: 99%

“…The problems emerging can be seen best in the expressions for the free energy F as calculated in various theoretical models. The most exhaustive calculations, up to ∼ g 5 , have been performed for the massless φ 4 theory [5,6] and for QCD (without and with quarks) [7,8]. These results have the following unpleasant features:…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Resummations of free energy at high temperature

Cvetič

Kögerler

2002

Phys. Rev. D

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We discuss resummation strategies for free energy in quantum field theories at nonzero temperatures T . We point out that resummations should be performed for the short-and long-distance parts separately in order to avoid spurious interference effects and double-counting. We then discuss and perform Padé resummations of these two parts for QCD at high T . The resummed results are almost invariant under variation of the renormalization and factorization scales. We perform the analysis also in the case of the massless scalar φ 4 theory.

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The free energy of hot QED at fifth order

Parwani

1994

Physics Letters B

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The order e 5 contribution to the pressure of massless quantum electrodynamics at nonzero temperature is determined explicitly. An identity is also obtained relating a gauge-invariant piece of the pressure at order e 2n+3 (n ≥ 1) (from diagrams with only one fermion loop) to the pressure at order e 2n . Prospects for higher order calculations are discussed and potential applications are mentioned. *

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Pressure in thermal scalar field theory to three-loop order

Abstract: In scalar field theory, with a g244 interaction, at temperature Twe compute the complete contribution to the pressure to order g4. This involves a three-loop thermal diagram. We neglect the zerotemperature mass.PACS number(s): 1 l. lO.Ef,

Cited by 55 publications

References 6 publications

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

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

Resummations of free energy at high temperature

The free energy of hot QED at fifth order

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