Resummation in Hot Field Theories

Abstract

There has been significant progress in our understanding of finite-temperature field theory over the past decade. In this paper, we review the progress in perturbative thermal field theory focusing on thermodynamic quantities. We first discuss the breakdown of naive perturbation theory at finite temperature and the need for an effective expansion that resums an infinite class of diagrams in the perturbative expansion. This effective expansion which is due to Braaten and Pisarski, can be used to systematically calculate various static and dynamical quantities as a weak-coupling expansion in powers of g. However, it turns that the weak-coupling expansion for thermodynamic quantities are useless unless the coupling constant is very small. We critically discuss various ways of reorganizing the perturbative series for thermal field theories in order to improve its convergence. These include screened perturbation theory (SPT), hard-thermal-loop perturbation theory (HTLPT), the Phi-derivable approach, dimensionally reduced (DR) SPT, and the DR Phi-derivable approach.

82 pages, 20 figures; v2 - typos corrected, references added

References in corpus (91)

• Thermodynamics of SU(3) Lattice Gauge Theory
• Critical point of QCD at finite T and μ, lattice results for physical quark masses
• The QCD phase diagram for small densities from imaginary chemical potential
• Lattice determination of the critical point of QCD at finite T and μ
• The QCD thermal phase transition in the presence of a small chemical potential
• Finite density QCD via imaginary chemical potential
• A new method to study lattice QCD at finite temperature and chemical potential
• The pressure of hot QCD up to g^6 ln(1/g)
• Free Energy of QCD at High Temperature
• The Equation of State for Two Flavor QCD at Non-zero Chemical Potential
• Phases of dense matter in neutron stars
• Quark-Gluon Plasma as a Condensate of Z(3) Wilson Lines
• Approximately self-consistent resummations for the thermodynamics of the quark-gluon plasma. I. Entropy and density
• Effective Field Theory Approach to High-Temperature Thermodynamics
• Small, Dense Quark Stars from Perturbative QCD
• 3D Physics and the Electroweak Phase Transition: Perturbation Theory
• Massive gluons and quarks and the equation of state obtained from SU(3) lattice QCD
• The Three-Loop Free Energy for Pure Gauge QCD
• The Three-Loop Free Energy for High-Temperature QED and QCD with Fermions
• The Free Energy of Hot Gauge Theories with Fermions Through g^5
• Screened Perturbation Theory
• The Equation of State of Deconfined Matter at Finite Chemical Potential in a Quasiparticle Description
• Hard-thermal-loop Resummation of the Free Energy of a Hot Gluon Plasma
• Pressure and non-linear susceptibilities in QCD at finite chemical potentials
• The entropy of the QCD plasma
• Far-from-equilibrium dynamics with broken symmetries from the 2PI-1/N expansion
• Equation of State for the SU(3) Gauge Theory
• The pressure of QCD at finite temperatures and chemical potentials
• The QCD equation of state at nonzero densities: lattice result
• Phenomenological Equations of State for the Quark-Gluon Plasma
• The Nonabelian Debye Mass at Next-to-Leading Order
• Advances in perturbative thermal field theory
• The non-Abelian Debye screening length beyond leading order
• Deconfining Phase Transition as a Matrix Model of Renormalized Polyakov Loops
• Optimized Perturbation Theory at Finite Temperature
• Variational perturbation expansion for strong-coupling coefficients of the anharmonic oscillator
• n-Particle irreducible effective action techniques for gauge theories
• From QCD lattice calculations to the equation of state of quark matter
• 3d physics and the electroweak phase transition: a framework for lattice Monte Carlo analysis
• HTL Perturbation Theory to Two Loops
• On the Apparent Convergence of Perturbative QCD at High Temperature
• Self-consistent hard-thermal-loop thermodynamics for the quark-gluon plasma
• Non-perturbative Debye mass in finite T QCD
• Hard-thermal-loop Resummation of the Thermodynamics of a Hot Gluon Plasma
• How to resum long-distance contributions to the QCD pressure?
• On the Convergence of Perturbative QCD at High Temperature
• The first second of the Universe
• Renormalization of Φ-derivable approximations in scalar field theories
• Screened Perturbation Theory to Three Loops
• Hard-thermal-loop Resummation of the Free Energy of a Hot Quark-Gluon Plasma
• Gauge-fixing dependence of Phi-derivable approximations
• Nonabelian Debye Screening in One-Loop Resummed Perturbation Theory
• The equation of state for two flavor QCD at N_t=6
• The Electroweak Phase Transition at $m_H\simeq m_W$
• Four-loop vacuum energy density of the SU(N_c) + adjoint Higgs theory
• The Little Bang: Searching for quark-gluon matter in relativistic heavy-ion collisions
• Thermodynamics of lattice QCD with two light quark flavours on a 16^3 x 8 lattice II
• Self-consistent approximations in relativistic plasmas: Quasiparticle analysis of the thermodynamic properties
• Resummations in Hot Scalar Electrodynamics
• Thermodynamics of Four-Flavour QCD with Improved Staggered Fermions
• Renormalizability of Phi-derivable approximations in scalar phi^4 theory
• HTL quasiparticle models of deconfined QCD at finite chemical potential
• HTL Resummation of the Thermodynamic Potential
• Thermodynamics of the high-temperature quark-gluon plasma
• The Equation of State for Dense QCD and Quark Stars
• Mass Expansions of Screened Perturbation Theory
• 2PI effective action and gauge invariance problems
• The Pressure of Hot $g^2{\varphi }^4$ Theory at order $g^5$
• Quasiparticle Description of the QCD Plasma, Comparison with Lattice Results at Finite T and Mu
• Transport coefficients from the 2PI effective action
• On the screening of static electromagnetic fields in hot QED plasmas
• The thermal heat kernel expansion and the one-loop effective action of QCD at finite temperature
• Comment on ``High Temperature Fermion Propagator -- Resummation and Gauge Dependence of the Damping Rate''
• The Massive Thermal Basketball Diagram
• The Free Energy of Hot QED at Fifth Order
• Solution to the 3-Loop $\Phi$-Derivable Approximation for Massless Scalar Thermodynamics
• Higher Order Corrections to the Equation of State of QED at High Temperature
• Solution to the 3-loop $\Phi$-derivable Approximation for Scalar Thermodynamics
• Pade Improvement of the Free Energy in High Temperature QCD
• Perturbative Finite-Temperature Results and Pad'e Approximants
• The Three Loop Equation of State of QED at High Temperature
• Gauge Dependence of the Resummed Thermal Gluon Self Energy
• The Free Energy of High Temperature QED to Order $e^5$ From Effective Field Theory
• Covariant derivative expansion of Yang-Mills effective action at high temperatures
• Borel Resummation of the Perturbative Free Energy of Hot Yang-Mills Theory
• Resummations of free energy at high temperature
• The Free Energy Of Hot Gauge Theories
• Covariant derivative expansion of fermionic effective action at high temperatures
• Electronic contribution to the oscillations of a gravitational antenna
• Relativistic Heavy-Ion Physics: Experimental Overview
• Equation of State in Quantum Chromodynamics

Cited by in corpus (110)

• Cold Quark Matter
• Physics of Strongly coupled Quark-Gluon Plasma
• Hard-Loop Dynamics of Non-Abelian Plasma Instabilities
• Jet physics in heavy-ion collisions
• Dynamics of Quark-Gluon-Plasma Instabilities in Discretized Hard-Loop Approximation
• Three-loop HTL QCD thermodynamics
• Effective Theory of Wilson Lines and Deconfinement
• Relativistic anisotropic hydrodynamics
• Three-loop HTLpt Pressure and Susceptibilities at Finite Temperature and Density
• NNLO hard-thermal-loop thermodynamics for QCD
• On the perturbative expansion at high temperature and implications for cosmological phase transitions
• Equation of State of hot and dense QCD: Resummed perturbation theory confronts lattice data
• Fuzzy Bags and Wilson Lines
• Gluon Thermodynamics at Intermediate Coupling
• Renormalized thermodynamics from the 2PI effective action
• Non-perturbative thermal flows and resummations
• QCD matter in extreme environments
• Robust approach to thermal resummation: Standard Model meets a singlet
• Shifted-Action Expansion and Applicability of Dressed Diagrammatic Schemes
• Three-loop HTL gluon thermodynamics at intermediate coupling
• Gluon screening mass at finite temperature from Landau gauge gluon propagator in lattice QCD
• Effective field theory approach to thermal bubble nucleation
• Equation of state of the SU($3$) Yang-Mills theory: a precise determination from a moving frame
• Pion and Kaon Condensation at Finite Temperature and Density
• Massless Mode and Positivity Violation in Hot QCD
• Two-loop HTL pressure at finite temperature and chemical potential
• Perturbation theory and non-perturbative renormalization flow in scalar field theory at finite temperature
• Theory of quantum impurities in spin liquids
• Constraining relativistic viscous hydrodynamical evolution
• Small shear viscosity in the semi quark gluon plasma
• Four-loop pressure of massless O(N) scalar field theory
• Quasiparticle equation of state for anisotropic hydrodynamics
• Stabilizing perturbative Yang-Mills thermodynamics with Gribov quantization
• QCD Equation of State at Finite Chemical Potentials for Relativistic Nuclear Collisions
• Four-loop screened perturbation theory
• Hard thermal loops, to quadratic order, in the background of a spatial 't Hooft loop
• Strange hadron production in heavy ion collisions from SPS to RHIC
• α_S from $F_{\pi }$ and Renormalization Group Optimized Perturbation
• Trace Anomaly, Thermal Power Corrections and Dimension Two condensates in the deconfined phase
• Real scalar phase transitions: a nonperturbative analysis
• Quasiparticle anisotropic hydrodynamics for central collisions
• Transport coefficients of the Gribov-Zwanziger plasma
• Asymptotic thermal quark masses and the entropy of QCD in the large-N_f limit
• A renormalization group approach for QCD in a strong magnetic field
• The QCD trace anomaly
• Variational approach to Yang-Mills theory at finite temperatures
• Applicability of the Linear delta Expansion for the lambda phi^4 Field Theory at Finite Temperature in the Symmetric and Broken Phases
• 2PI effective action for gauge theories: Renormalization
• Causal Viscous Hydrodynamics for Relativistic Heavy Ion Collisions
• Pressure to order $g^8\ast log(g)$ in ${\varphi }^4$-theory at weak coupling
• Bottomonium suppression and elliptic flow using Heavy Quarkonium Quantum Dynamics
• A brief overview of hard-thermal-loop perturbation theory
• Renormalization Group Optimized Perturbation Theory at Finite Temperatures
• Scale Invariant Resummed Perturbation at Finite Temperatures
• Cold Quark Matter, Quadratic Corrections and Gauge/String Duality
• Three-loop HTL Free Energy for QED
• Eigenvalue repulsion in an effective theory of SU(2) Wilson lines in three dimensions
• The pressure of QED from the two-loop 2PI effective action
• NNLO HTLpt predictions for the curvature of the QCD phase transition line
• Ward Identities for the 2PI effective action in QED
• Geometrically confined thermal field theory: Finite size corrections and phase transitions
• Higher mass limits of neutron stars from the equation of states in curved spacetime
• Covariant kinetic theory and transport coefficients for Gribov plasma
• Reliability of the optimized perturbation theory in the 0-dimensional $O(N)$ scalar field model
• Magnetic confinement and the Linde problem
• Beta-functions for a SU(2) Matrix Model in 2 + epsilon Dimensions
• Study of the gluon propagator in the large-N_f limit at finite temperature and chemical potential for weak and strong couplings
• Two-loop effective potential, thermal resummation and first-order phase transitions: Beyond the high-temperature expansion
• Hubble-induced mass from MSSM plasma
• Parton self-energies for general momentum-space anisotropy
• QCD pressure: renormalization group optimized perturbation theory confronts lattice
• The Powers of Deconfinement
• QCD mesonic screening masses using Gribov quantization
• The O(2) model in polar coordinates at nonzero temperature
• Trace Anomaly and dimension two gluon condensate above the phase transition
• Coulomb gauge Yang-Mills theory at finite temperatures: glueballs versus quasi-gluons
• The asymmetry of the dimension 2 gluon condensate: the finite temperature case
• Asymptotically Free Theory with Scale Invariant Thermodynamics
• Nuclear and Quark Matter at High Temperature
• Recent progress in hard-thermal-loop QCD thermodynamics and collective excitations
• Massive renormalization scheme and perturbation theory at finite temperature
• $\mathcal{N}=4$ supersymmetric Yang-Mills thermodynamics to order ${\lambda }^2$
• Renormalization group improved pressure for hot and dense quark matter
• Semiclassical thermodynamics of scalar fields
• Covariant formulation of gluon self-energy in presence of ellipsoidal anisotropy
• Effective potential for Polyakov loops from a center symmetric effective theory in three dimensions
• Renormalization group optimized $\lambda {\varphi }^4$ pressure at next-to-next-to-leading order
• On the (in)consistency of perturbation theory at finite temperature
• Hard-loop dynamics of non-abelian plasma instabilities
• Polyakov loop, gluon mass, gluon condensate and its asymmetry near deconfinement
• Shear and bulk viscosity of quark-gluon plasma with Gribov gluons and quasiparticle quarks
• Linde problem in Yang-Mills theory compactified on ${\mathbb{R}}^2\times {\mathbb{T}}^2$
• Equation of State for QCD at finite temperature and density. Resummation versus lattice data
• Two-loop free energy of three-dimensional antiferromagnets in external magnetic and staggered fields
• Visualizing Color Plasma Instabilities
• Quantum statistical correlations in thermal field theories: boundary effective theory
• Hard loop effective theory of the (anisotropic) quark gluon plasma
• NLO Dispersion Laws for Slow-Moving Quarks in HTL QCD
• Zero-mode analysis of quantum statistical physics
• Lattice simulation of a center symmetric three-dimensional effective theory for SU(2) Yang-Mills
• Pressure of massless hot scalar theory in the boundary effective theory framework
• Quantum critical dynamics for a prototype class of insulating antiferromagnets
• Distribution of solutions of the fastest apparent convergence condition in optimized perturbation theory and its relation to anti-Stokes lines
• Finite size effects in the phase transition patterns of coupled scalar field systems
• Effective potential in the BET formalism
• Finite System Size Correction to the Effective Coupling in ${\varphi }^4$ Scattering
• Non-perturbative constraints on perturbation theory at finite temperature
• Hard-thermal-loop QED thermodynamics
• Thermodynamics of QCD at large quark chemical potential
• Scale dependence improvement of the quartic scalar field thermal effective potential in the optimized perturbation theory