Classical lattice gauge fields with hard thermal loops

Hu, C. R.; Müller, Berndt

doi:10.1016/s0370-2693(97)00851-4

Cited by 63 publications

(80 citation statements)

References 23 publications

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“…1.6). Remarkably, the results obtained in this way, even without any matching, appear to be rather insensitive to lattice artifacts, and are moreover consistent with some previous numerical calculations [57] (where the HTL's are simulated via classical coloured "test particles" [54]), and also with the theoretical predictions in Refs. [78,25].…”

Section: Effective Classical Thermal Field Theorysupporting

confidence: 90%

“…(See also Refs. [57,58] for a different lattice implementation of the HTL effects, and Refs. [79,80,81,82] for numerical calculations within purely Yang-Mills classical theory, without HTL's.…”

Section: Effective Theory For Soft and Ultrasoft Excitationsmentioning

confidence: 99%

“…[57,28,157]), and applied to the calculation of the anomalous baryon number violation rate in a high-temperature Yang-Mills theory (cf. Sect.…”

Section: Effective Classical Thermal Field Theorymentioning

confidence: 99%

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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: Effective Classical Thermal Field Theorysupporting

confidence: 90%

Section: Effective Theory For Soft and Ultrasoft Excitationsmentioning

confidence: 99%

See 1 more Smart Citation

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

Blaizot¹,

Iancu²

2002

Physics Reports

515

714

View full text Add to dashboard Cite

show abstract

“…(The hard thermal loops are the nonabelian generalization of Debye screening, Landau damping, and other plasma effects familiar from electromagnetic plasmas.) Such a classical, but HTL including, treatment should be correct at leading order in the coupling g. Two numerical implementations of such a classical theory now exist; one [39] is based on a proposal by Hu and Müller [40], and one [17] is based on a proposal by Bödeker, McLerran, and Smilga [36], and more recently discussed by Iancu [41]. Both are extremely complicated.…”

Section: B Dynamics: Classical Effective Theoriesmentioning

confidence: 99%

Electroweak bubble nucleation, nonperturbatively

2001

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We present a lattice method to compute bubble nucleation rates at radiatively induced first order phase transitions, in high temperature, weakly coupled field theories, nonperturbatively. A generalization of Langer's approach, it makes no recourse to saddle point expansions and includes completely the dynamical prefactor. We test the technique by applying it to the electroweak phase transition in the minimal standard model, at an unphysically small Higgs mass which gives a reasonably strong phase transition (λ/g 2 = 0.036, which corresponds to m H /m W = 0.54 at tree level but does not correspond to a positive physical Higgs mass when radiative effects of the top quark are included), and compare the results to older perturbative and other estimates. While two loop perturbation theory slightly under-estimates the strength of the transition measured by the latent heat, it over-estimates the amount of supercooling by a factor of 2.

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“…In recent years, Wong's equations for classical charged particles interacting with classical non-Abelian gauge fields have received a considerable amount of attention in finite temperature applications [25,26,31]. Wong wrote down the following set of equations [9] m dx µ…”

Section: Wong's Equations and The World Line Lagrangianmentioning

confidence: 99%

Minding one’s P’s and Q’s: From the one loop effective action in quantum field theory to classical transport theory

et al. 2000

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The one loop effective action in quantum field theory can be expressed as a quantum mechanical path integral over world lines, with internal symmetries represented by Grassmanian variables. In this paper, we develop a real time, many body, world line formalism for the one loop effective action. In particular, we study hot QCD and obtain the classical transport equations which, as Litim and Manuel have shown, reduce in the appropriate limit to the non-Abelian Boltzmann-Langevin equation first obtained by Bödeker. In the Vlasov limit, the classical kinetic equations are those that correspond to the hard thermal loop effective action. We also discuss the imaginary time world line formalism for a hot φ 4 theory, and elucidate its relation to classical transport theory. IntroductionIn classical kinetic theory, a covariant formalism can be obtained in terms of phase space averages over the trajectories of particle world lines [1]. In quantum field theory, there are many instances at finite temperature and density where classical ideas are relevant, and where a classical kinetic picture would be useful. However, it is not immediately apparent how one recovers the classical world line picture directly from quantum field theory. This is especially problematic in theories with internal symmetries.Fortunately, in the last decade, there has been a considerable body of work relating the one loop effective action in quantum field theory to quantum mechanical path integrals over point particle Lagrangians 1 . For a survey of recent developments, see the review by Schubert [4]. These recent developments follow from the key insight by Berezin and Marinov [5] that internal symmetries such as color and spin had classical analogues in terms of Grassmanian variables. These obeyed classical commutation relations which, when quantized, gave the usual commutation relations for spin and color.Brink, DiVecchia, and Howe used these Grassmanian variables to construct a classical Lagrangian for spinning world lines in an Abelian background field [6]. Subsequently, Balachandran et al. [7] and Barducci et al. [8] wrote down the following Lagrangian for a classical colored particle in a non-Abelian background field 2 :Here the λ a (τ ) with a = 1, · · · , N are Grassmanian dynamical variables, and D ab λ b =λ a + igẋ µ A α µ T α ab λ b . The variables T α ab 's are N × N matrices in an irreducible representation of the Lie algebra of the group. The EulerLagrange equations of motion are deduced in the usual way from the above Lagrangian. It was shown by Balachandran et al. and by Barducci et al. that these equations are precisely the equations written down nearly thirty years ago by S.K. Wong [9].The connection of the work on point particle Lagrangians to quantum field theory was first made by Strassler [10]. He showed that the one loop effective action in quantum field theory could be expressed in terms of a quantum mechanical path integral over a point particle Lagrangian. For an Abelian gauge theory, Strassler showed that this Lag...

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Classical lattice gauge fields with hard thermal loops

Cited by 63 publications

References 23 publications

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

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

Electroweak bubble nucleation, nonperturbatively

Minding one’s P’s and Q’s: From the one loop effective action in quantum field theory to classical transport theory

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