Classical theory for non-perturbative dynamics in hot QCD
I present an effective classical theory which describes the non-perturbative real-time dynamics in hot gauge theories and has the potential for numerical implementation.
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arXiv subjects
Edmond Iancu
Publications and source records attributed to Edmond Iancu.
Classical effective theory for hot QCD
In high temperature QCD, the perturbation theory is plagued with infrared divergences which reflect long-range non-perturbative phenomena. I argue that it is possible to study such phenomena within a classical thermal field theory which can be put on a three-dimensional lattice. The classical theory is an effective theory for the soft, non-perturbative modes, as obtained after integrating out the hard modes in perturbation theory. It is well suited for numerical studies of the non-perturbative real-time dynamics, which cannot be studied within the standard, imaginary-time formulations of lattice QCD.
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Effective theory for real-time dynamics in hot gauge theories
For a high temperature non-Abelian plasma, we reformulate the hard thermal loop approximation as an effective classical thermal field theory for the soft modes. The effective theory is written in local Hamiltonian form, and the thermal partition function is explicitly constructed. It involves an ultraviolet cutoff which separates between hard and soft degrees of freedom in a gauge-invariant way, together with counterterms which cancel the cutoff dependence in the soft correlation functions. The effective theory is well suited for numerical studies of the non-perturbative dynamics in real time, in particular, for the computation of the baryon number violation rate at high temperature.
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The Bloch-Nordsieck propagator at finite temperature
We have shown recently that the resummation of soft photon contributions leads to a non-exponential decay of the fermion excitations in hot QED plasmas. The retarded propagator of a massless fermion was found to behave as $S_R(t >> 1/gT) \sim \exp{-αT t [\ln(ω_p t) + C]}$, where $ω_p=gT/3$ is the plasma frequency, $α=g^2/4π$, and $C$ is a constant, independent of $g$, which was left undefined. This term is computed in this paper. In gauges with unphysical degrees of freedom, it is gauge-fixing independent provided an infrared regulator is introduced in the gauge sector. We also extend our analysis to hot QCD and express the quark and gluon propagators in the form of three-dimensional Euclidean functional integrals which may be evaluated on the lattice.
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High Temperature QCD
I discuss finite-temperature gauge theories as a framework to describe the quark-gluon plasma in the regime of high temperature where the gauge coupling is small, $g << 1$. I review recent progress in the understanding of the long-range physics, with emphasis on the collective phenomena and their consequences for the screening of the gauge interactions. I consider some of the infrared divergences of the perturbation theory, and discuss the physical mechanisms which remove these divergences.
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The quasiparticle structure of hot gauge theories
The study of the ultrarelativistic plasmas in perturbation theory is plagued with infrared divergences which are not eliminated by the screening corrections. They affect, in particular, the computation of the lifetime of the elementary excitations, thus casting doubt on the validity of the quasiparticle picture. We show that, for Abelian plasmas at least, the infrared problem of the damping rate can be solved by a non-perturbative treatment based on the Bloch-Nordsieck approximation. The resulting expression of the fermion propagator is free of divergences, and exhibits a {\it non-exponential} damping at large times: $S_R(t)\sim \exp\{-αT t \lnω_pt\}$, where $ω_p=gT/3$ is the plasma frequency and $α=g^2/4π$.
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Lifetime of quasiparticles in hot gauge theories
The perturbative calculation of the lifetime of charged excitations in ultrarelativistic plasmas is plagued with infrared divergences which are not eliminated by the screening corrections. The physical processes responsible for these divergences are the collisions involving the exchange of longwavelength, quasistatic, magnetic gluons (or photons), which are not screened by plasma effects. In QED, the leading divergences can be resummed in a non-perturbative treatement based on a generalization of the Bloch-Nordsieck model at finite temperature. The resulting expression of the fermion propagator is free of infrared problems, and exhibits a ``non-exponential'' damping at large times: $S_R(t)\sim exp {-αT t lnω_pt}$, where $ω_p=eT/3$ is the plasma frequency and $α=e^2/4π$.
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Lifetimes of quasiparticles and collective excitations in hot QED plasmas
The perturbative calculation of the lifetime of fermion excitations in a QED plasma at high temperature is plagued with infrared divergences which are not eliminated by the screening corrections. The physical processes responsible for these divergences are the collisions involving the exchange of longwavelength, quasistatic, magnetic photons, which are not screened by plasma effects. The leading divergences can be resummed in a non-perturbative treatement based on a generalization of the Bloch-Nordsieck model at finite temperature. The resulting expression of the fermion propagator is free of infrared problems, and exhibits a {\it non-exponential} damping at large times: $S_R(t)\sim \exp\{-αT t \lnω_pt\}$, where $ω_p=eT/3$ is the plasma frequency and $α=e^2/4π$.
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Lifetime of quasiparticles in hot QED plasmas
The calculation of the lifetime of quasiparticles in a QED plasma at high temperature remains plagued with infrared divergences, even after one has taken into account the screening corrections. The physical processes responsible for these divergences are the collisions involving the exchange of very soft, unscreened, magnetic photons, whose contribution is enhanced by the thermal Bose-Einstein occupation factor. The self energy diagrams which diverge in perturbation theory contain no internal fermion loops, but an arbitrary number of internal magnetostatic photon lines. By generalizing the Bloch-Nordsieck model at finite temperature, we can resum all the singular contributions of such diagrams, and obtain the correct long time behaviour of the retarded fermion propagator in the hot QED plasma: $S_R(t)\sim \exp\{-αT \, t\, \lnω_pt\}$, where $ω_p=eT/3$ is the plasma frequency and $α=e^2/4π$.
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On the screening of static electromagnetic fields in hot QED plasmas
We study the screening of static magnetic and electric fields in massless quantum electrodynamics (QED) and massless scalar electrodynamics (SQED) at temperature $T$. Various exact relations for the static polarisation tensor are first reviewed and then verified perturbatively to fifth order (in the coupling) in QED and fourth order in SQED, using different resummation techniques. The magnetic and electric screening masses squared, as defined through the pole of the static propagators, are also calculated to fifth order in QED and fourth order in SQED, and their gauge-independence and renormalisation-group invariance is checked. Finally, we provide arguments for the vanishing of the magnetic mass to all orders in perturbation theory.
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QCD Transport Theory
Because of the long range of the gauge interactions, the collective behaviour of quarks and gluons plays a decisive role in the transport processes. Collective effects, like Debye screening and Landau damping, remove the unphysical infrared divergences of the transport cross-sections and provide finite relaxation rates. I review here a theory of the plasma collective excitations that has been recently developed. It is based on kinetic equations derived from the general QCD Dyson-Schwinger equations, in the weak coupling limit. I present new, truly non-abelian, collective excitations, which correspond to nonlinear color oscillations of the QCD plasma.
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Gauge Structure and Semi-Classical Aspects of Hard Thermal Loops
Hard thermal loops play a central role in the theory of long wavelength excitations of a quark-gluon plasma. We show in this paper how our recent derivation of their generating functional from the Dyson-Schwinger equations sheds light on their semi-classical nature and their remarkable gauge structure. In particular, we show that our kinetic equations can be written in terms of auxiliary gauge fields with zero curvature. Remarkably, the latter property determines entirely the dynamics in the kinematical regime of hard thermal loops. This explains in particular why the generating functional could have been obtained by Taylor and Wong from gauge invariance considerations. It also clarifies the role of Chern-Simons theory in this context.
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Non-Abelian Plane-Waves in the Quark-Gluon Plasma
We present new, non-abelian, solutions to the equations of motion which describe the collective excitations of a quark-gluon plasma at high temperature. These solutions correspond to longitudinal and transverse plane-waves propagating through the plasma.
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Energy-Momentum Tensors for the Quark-Gluon Plasma
We construct the energy-momentum tensor for the gauge fields which describe the collective excitations of the quark-gluon plasma. We rely on the description of the collective modes that we have derived in previous works. By using the conservation laws for energy and momentum, we obtain three different versions for the tensor $T^{μν}$, which are physically equivalent. We show that the total energy constructed from $T^{00}$ is positive for any non-trivial field configuration. Finally, we present a new non-abelian solution of the equations of motion for the gauge fields. This solution corresponds to spatially uniform color oscillations of the plasma.
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Non-Abelian Excitations of the Quark-Gluon Plasma
We present new, non-abelian, solutions to the equations of motion which describe the collective excitations of a quark-gluon plasma at high temperature. These solutions correspond to spatially uniform color oscillations.
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Soft Fields and Hard Particles in Hot Gauge Plasmas
It is shown that the long wavelength excitations of a quark-gluon plasma may be described as collective oscillations of self-consistent average fields to which the plasma particles couple. Their properties are obtained from a set of coupled mean field and kinetic equations, derived from the general Dyson-Schwinger equations, as the leading order in a systematic expansion in powers of the coupling. By solving the kinetic equations, one obtains in closed form the generating functionals for all the leading order amplitudes between soft quasiparticles, the so-called ``hard thermal loops''.
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