Renormalization of Self-consistent Approximation schemes Finite Temperature II: Applications to the Sunset Diagram

Abstract

The theoretical concepts for the renormalization of self-consistent Dyson resummations, deviced in the first paper of this series, are applied to first example cases for the ${\varphi }^4$-theory. Besides the tadpole (Hartree) approximation as a novel part the numerical solutions are presented which includes the sunset self-energy diagram into the self-consistent scheme based on the $\Phi$-derivable approximation or 2PI effective action concept.

18 pages, 7 figures Changes in version 2: Adapted title to the first paper of the series, added one figure and some references. This version was submitted to Phys. Rev. D; Changes in version 3: added one more reference Changes in version 4 (accepted for publication by Phys. Rev. D): Added a paragraph about the massless case and some remarks in the introduction

References in corpus (3)

• Controlled nonperturbative dynamics of quantum fields out of equilibrium
• Renormalization in Self-Consistent Approximations schemes at Finite Temperature I: Theory
• Nonequilibrium time evolution of the spectral function in quantum field theory

Cited by in corpus (107)

• Far-from-equilibrium dynamics with broken symmetries from the 2PI-1/N expansion
• Advances in perturbative thermal field theory
• Critical Points in the Linear Sigma Model with Quarks
• Nonperturbative renormalization for 2PI effective action techniques
• HTL Perturbation Theory to Two Loops
• Quantum dynamics and thermalization for out-of-equilibrium phi^4-theory
• On the Apparent Convergence of Perturbative QCD at High Temperature
• Renormalization in Self-Consistent Approximation schemes at Finite Temperature III: Global Symmetries
• Nonequilibrium chiral fluid dynamics including dissipation and noise
• Tachyonic preheating using 2PI-1/N dynamics and the classical approximation
• Renormalization of Φ-derivable approximations in scalar field theories
• Chiral symmetry restoration in linear sigma models with different numbers of quark flavors
• Equilibration in phi^4 theory in 3+1 dimensions
• Gauge-fixing dependence of Phi-derivable approximations
• Nonequilibrium Quantum-Field Dynamics and Off-Shell Transport for ${\varphi }^4$-theory in 2+1 dimensions
• Renormalized thermodynamics from the 2PI effective action
• Shear Viscosity in the O(N) Model
• Renormalizability of Phi-derivable approximations in scalar phi^4 theory
• Two-loop HTL Thermodynamics with Quarks
• HTL quasiparticle models of deconfined QCD at finite chemical potential
• Quantum dynamics of phase transitions in broken symmetry $\lambda {\varphi }^4$ field theory
• Pion and Kaon Condensation at Finite Temperature and Density
• Role of Fluctuations in the Linear Sigma Model with Quarks
• Kadanoff-Baym Equations with Non-Gaussian Initial Conditions: The Equilibrium Limit
• Hard gluon damping in hot QCD
• Equilibration and relaxation times at the chiral phase transition including reheating
• Four-loop screened perturbation theory
• Transport coefficients from the 2PI effective action
• Comparison of Boltzmann Equations with Quantum Dynamics for Scalar Fields
• Gapless Hartree-Fock Resummation Scheme for the O(N) Model
• Renormalization group methods and the 2PI effective action
• Transport coefficients in large N_f gauge theories with massive fermions
• Renormalizing the Schwinger-Dyson equations in the auxiliary field formulation of $\lambda {\varphi }^4$ field theory
• Decoherence in an Interacting Quantum Field Theory: The Vacuum Case
• Asymptotic thermal quark masses and the entropy of QCD in the large-N_f limit
• Renormalization group approach to interacting fermion systems in the two-particle-irreducible formalism
• Constraining the effective action by a method of external sources
• Bulk Viscosity at Extreme Limits: From Kinetic Theory to Strings
• The O(N) linear sigma model at finite temperature beyond the Hartree approximation
• Isotropization far from equilibrium
• Applicability of the Linear delta Expansion for the lambda phi^4 Field Theory at Finite Temperature in the Symmetric and Broken Phases
• The 2PI effective theory at next-to-leading order using the functional renormalization group
• 2PI effective action for gauge theories: Renormalization
• Influence of the Polyakov loop on the chiral phase transition in the two flavor chiral quark model
• Symmetry-Improved 2PI Approach to the Goldstone-Boson IR Problem of the SM Effective Potential
• Functional renormalization group and 2PI effective action formalism
• Self-consistent Approach to Off-Shell Transport
• 2PI functional techniques for gauge theories: QED
• Renormalisability of the 2PI-Hartree approximation of multicomponent scalar models in the broken symmetry phase
• Gauge theories on hyperbolic spaces and dual wormhole instabilities
• Renormalised nonequilibrium quantum field theory: scalar fields
• Self-consistent description of vector-mesons in matter
• The 2PI effective action at four loop order in ${\phi }^4$ theory
• Renormalized broken-symmetry Schwinger-Dyson equations and the 2PI-1/N expansion for the O(N) model
• Selfconsistent calculations of spectral densities in the O(N) model: improving the Hartree-Fock approximation by including nonzero decay widths
• Three-loop Phi-derivable Approximation in QED
• Renormalization of a gapless Hartree-Fock approximation to a theory with spontaneously broken O(N)-symmetry
• Looking for defects in the 2PI correlator
• Next-to-Leading Order Transport Coefficients from the Four-Particle Irreducible Effective Action
• Broken phase scalar effective potential and Phi-derivable approximations
• Delta(1232) and Nucleon Spectral Functions in Hot Hadronic Matter
• Renormalization group flow equations connected to the $n$PI effective action
• Broken phase effective potential in the two-loop Phi-derivable approximation and nature of the phase transition in a scalar theory
• The pressure of QED from the two-loop 2PI effective action
• Ward Identities for the 2PI effective action in QED
• Non-equilibrium dynamics of a scalar field with quantum backreaction
• Nonperturbative renormalization of Phi-derivable approximations in theories with fermions
• Non-perturbative finite $T$ broadening of the $\rho$ meson and dilepton emission in heavy ion-collisions
• Thermal effects on slow-roll dynamics
• Entropy production in 2D $\lambda {\varphi }^4$ theory in the Kadanoff-Baym approach
• Selfconsistent approximations, symmetries and choice of representation
• Bethe-Salpeter Equations from the 4PI effective action
• Effective convergence of the 2PI-1/N expansion for nonequilibrium quantum fields
• Exact RG Invariance and Symmetry Improved 2PI Effective Potential
• Hadron Liquid with a Small Baryon Chemical Potential at Finite Temperature
• On the thermal sunset diagram for scalar field theories
• Counterterm resummation for 2PI-approximation in constant background
• Renormalization of O(N) model in 1/N expansion in auxiliary field formalism
• 4-point vertices from the 2PI and 4PI Effective Actions
• Study of chiral symmetry restoration in linear and nonlinear O(N) models using the auxiliary field method
• Non-equilibrium quantum mechanics: A 'hot quantum soup' of paramagnons
• On the symmetry improved CJT formalism in the $O(4)$ linear sigma model
• Nonequilibrium evolution of Phi**4 theory in 1+1 dimensions in the 2PPI formalism
• Resummations in the Bloch-Nordsieck model
• Kaon condensation in the color-flavor-locked phase of quark matter, the Goldstone theorem, and the 2PI Hartree approximation
• Renormalization of 2PI resummation: a renormalization scheme approach
• Single-particle spectral function for the classical one-component plasma
• Padé approximants and analytic continuation of Euclidean Phi-derivable approximations
• A new method to calculate the n-Particle Irreducible Effective Action
• Renormalization of the 4PI effective action using the functional renormalization group
• The effect of memory on relaxation in a scalar field theory
• The 2PI finite temperature effective potential of the O(N) linear sigma model in 1+1 dimensions, at next-to-leading order in 1/N
• Renormalization in momentum dependent resummations
• On the (in)consistency of perturbation theory at finite temperature
• Broken symmetry phase solution of the phi^4 model at two-loop level of the Phi-derivable approximation
• Renormalisation of out-of-equilibrium quantum fields
• Dynamics of Resonances in Strongly Interacting Systems
• rho propagation and dilepton production at finite pion density and temperature
• Nonequilibrium dynamics and transport near the chiral phase transition of a quark-meson model
• Scaling violation and the magnetic equation of state in chiral models
• Kinetics of the chiral phase transition in a quark-meson $\sigma$-model
• The Delta(1232) at RHIC
• Zero point energy of composite particles: The medium effects
• Renormalization of the 2PI-Hartree approximation in a broken phase with nonzero superflow
• A new resummation scheme in scalar field theories
• Selfconsistent descriptions of vector-mesons in hot matter revisited
• Non-perturbative constraints on perturbation theory at finite temperature