Complete High Temperature Expansions for One-Loop Finite Temperature Effects

Abstract

We develop exact, simple closed form expressions for partition functions associated with relativistic bosons and fermions in odd spatial dimensions. These expressions, valid at high temperature, include the effects of a non-trivial Polyakov loop and generalize well-known high temperature expansions. The key technical point is the proof of a set of Bessel function identities which resum low temperature expansions into high temperature expansions. The complete expressions for these partition functions can be used to obtain one-loop finite temperature contributions to effective potentials, and thus free energies and pressures.

9 pages, RevTeX, no figures. To be published in Phys. Rev D. v2 has revised introduction and conclusions, plus a few typographical errors are corrected; v3 corrects one typo

References in corpus (1)

• Phenomenological Equations of State for the Quark-Gluon Plasma

Cited by in corpus (54)

• Deconfining Phase Transition as a Matrix Model of Renormalized Polyakov Loops
• Two-point functions for SU(3) Polyakov Loops near T_c
• Effective matrix model for deconfinement in pure gauge theories
• New Phases of SU(3) and SU(4) at Finite Temperature
• How Wide is the Transition to Deconfinement?
• Phase diagrams of SU(N) gauge theories with fermions in various representations
• Deconfinement in Matrix Models about the Gross--Witten Point
• Small shear viscosity in the semi quark gluon plasma
• Critical endpoint for deconfinement in matrix and other effective models
• An effective gluon potential and hybrid approach to Yang-Mills thermodynamics
• Non-perturbative volume-reduction of large-N QCD with adjoint fermions
• Polyakov Loops versus Hadronic States
• Chiral matrix model of the semi-Quark Gluon Plasma in QCD
• Complex Saddle Points and Disorder Lines in QCD at finite temperature and density
• Complex saddle points in QCD at finite temperature and density
• Critical Behavior of Non Order-Parameter Fields
• Glueball Dark Matter revisited
• Two-loop perturbative corrections to the thermal effective potential in gluodynamics
• Induced Universal Properties and Deconfinement
• Polyakov loop fluctuations and deconfinement in the limit of heavy quarks
• Effective potential for SU(2) Polyakov loops and Wilson loop eigenvalues
• Collisional energy loss above the critical temperature in QCD
• String Tension Scaling in High-Temperature Confined SU(N) Gauge Theories
• Schwinger Pair Production at Finite Temperature
• Gross-Witten-Wadia transition in a matrix model of deconfinement
• A PNJL Model for Adjoint Fermions with Periodic Boundary Conditions
• The Finite Temperature SU(2) Savvidy Model with a Non-trivial Polyakov Loop
• Phases of Gauge Theories
• Improved ring potential of QED at finite temperature and in the presence of weak and strong magnetic field
• Finite temperature Schwinger pair production in coexistent electric and magnetic fields
• Impact of a uniform magnetic field and nonzero temperature on explicit chiral symmetry breaking in QED: Arbitrary hierarchy of energy scales
• Beta-functions for a SU(2) Matrix Model in 2 + epsilon Dimensions
• The consequences of SU(3) colorsingletness, Polyakov Loop and Z(3) symmetry on a quark-gluon gas
• Partial Deconfinement in Color Superconductivity
• Exotic phases of finite temperature SU(N) gauge theories
• Zero interface tension at the deconfining phase transition for a matrix model of a $SU(\infty )$ gauge theory
• Matrix model for deconfinement in an SU(2) gauge theory in 2+1 dimensions
• Glueball dark matter, precisely
• Anisotropy of magnetized quark matter
• Confinement in a Higgs Model on $R^3\times S^1$
• Matrix model for deconfinement in a SU(Nc) gauge theory in 2+1 dimensions
• QCD in magnetic field, Landau levels and double-life of unbroken center-symmetry
• Phases of circle-compactified QCD with adjoint fermions at finite density
• Exotic phases of finite temperature SU(N) gauge theories with massive fermions: F, Adj, A/S
• PT Symmetry and QCD: Finite Temperature and Density
• Exact high temperature expansion of the one-loop thermodynamic potential with complex chemical potential
• A Phenomenological Treatment of Chiral Symmetry Restoration and Deconfinement
• Chiral MHD description of a perfect magnetized QGP using the effective NJL model in a strong magnetic field
• Quark Confinement and the Renormalization Group
• High Temperature Confinement in SU(N) Gauge Theories
• Confinement on $R^3\times S^1$: continuum and lattice
• PNJL model for adjoint fermions
• Massive Gauge Theory with Quasigluon for Hot $SU(N)$: Phase Transition and Thermodynamics
• Building models of quarks and gluons with an arbitrary number of colors using Cartan-Polyakov loops