Divergences in real-time classical field theories at nonzero temperature

Aarts, Gert; Nauta, B.J.; Weert, Chris G. van

doi:10.1103/physrevd.61.105002

Cited by 24 publications

(40 citation statements)

References 54 publications

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“…But, as we argue in this paper for the de Sitter case, for large internal momenta (≈ H or ≈ T ) problems arise for the classical approximation, e.g. in the thermal case involving Hard Thermal Loops [70].…”

Section: A3 Comparison With Thermal Field Theorymentioning

confidence: 99%

Classical approximation to quantum cosmological correlations

Meulen¹,

Smit²

2007

J. Cosmol. Astropart. Phys.

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Abstract:We investigate up to which order quantum effects can be neglected in calculating cosmological correlation functions after horizon exit. As a toy model, we study φ 3 theory on a de Sitter background for a massless minimally coupled scalar field φ. We find that for tree level and one loop contributions in the quantum theory, a good classical approximation can be constructed, but for higher loop corrections this is in general not expected to be possible. The reason is that loop corrections get non-negligible contributions from loop momenta with magnitude up to the Hubble scale H, at which scale classical physics is not expected to be a good approximation to the quantum theory. An explicit calculation of the one loop correction to the two point function, supports the argument that contributions from loop momenta of scale H are not negligible. Generalization of the arguments for the toy model to derivative interactions and the curvature perturbation leads to the conclusion that the leading orders of non-Gaussian effects generated after horizon exit, can be approximated quite well by classical methods. Furthermore we compare with a theorem by Weinberg. We find that growing loop corrections after horizon exit are not excluded, even in single field inflation.

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Section: A3 Comparison With Thermal Field Theorymentioning

confidence: 99%

Classical approximation to quantum cosmological correlations

Meulen¹,

Smit²

2007

J. Cosmol. Astropart. Phys.

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“…Thus, by writing 84) in eq. (3.72), and recalling that G ab eq = δ ab G eq , we can easily obtain the following relation between δǴ and δG, valid to leading order in g: 85) or, after a Wigner transform,…”

Section: Gauge-covariant Wigner Functionsmentioning

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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“…The continuum equilibrium theory is plagued by Rayleigh-Jeans divergences, and a renormalisation with local counterterms is not possible in general [37]. Moreover, the counterterms are temperature dependent, which makes a consistent out-of-equilibrium renormalisation impossible.…”

Section: Introductionmentioning

confidence: 99%

Low-cost fermions in classical field simulations

Borsányi

Hindmarsh

2009

Phys. Rev. D

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We discuss the possible extension of the bosonic classical field theory simulations to include fermions. This problem has been addressed in terms of the inhomogeneous mean field approximation by Aarts and Smit. By performing a stochastic integration of an equivalent set of equations we can extend the original 1+1 dimensional calculations so that they become feasible in higher dimensions. We test the scheme in 2 + 1 dimensions and discuss some classical applications with fermions for the first time, such as the decay of oscillons.

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Divergences in real-time classical field theories at nonzero temperature

Cited by 24 publications

References 54 publications

Classical approximation to quantum cosmological correlations

Classical approximation to quantum cosmological correlations

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

Low-cost fermions in classical field simulations

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