Renormalization in Self-Consistent Approximations schemes at Finite Temperature I: Theory

Abstract

Within finite temperature field theory, we show that truncated non-perturbative self-consistent Dyson resummation schemes can be renormalized with local counter-terms defined at the vacuum level. The requirements are that the underlying theory is renormalizable and that the self-consistent scheme follows Baym''s $\Phi$-derivable concept. The scheme generates both, the renormalized self-consistent equations of motion and the closed equations for the infinite set of counter terms. At the same time the corresponding 2PI-generating functional and the thermodynamical potential can be renormalized, in consistency with the equations of motion. This guarantees the standard $\Phi$-derivable properties like thermodynamic consistency and exact conservation laws also for the renormalized approximation schemes to hold. The proof uses the techniques of BPHZ-renormalization to cope with the explicit and the hidden overlapping vacuum divergences.

22 Pages 1 figure, uses RevTeX4. The Revision concerns the correction of some minor typos, a clarification concerning the real-time contour structure of renormalization parts and some comments concerning symmetries in the conclusions and outlook

References in corpus (1)

• Exact Conservation Laws of the Gradient Expanded Kadanoff-Baym Equations

Cited by in corpus (123)

• Aspects of the Functional Renormalisation Group
• Far-from-equilibrium dynamics with broken symmetries from the 2PI-1/N expansion
• Advances in perturbative thermal field theory
• n-Particle irreducible effective action techniques for gauge theories
• 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
• Renormalization of Self-consistent Approximation schemes Finite Temperature II: Applications to the Sunset Diagram
• 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
• Systematic approach to leptogenesis in nonequilibrium QFT: vertex contribution to the CP-violating parameter
• Chiral symmetry restoration in linear sigma models with different numbers of quark flavors
• Equilibration in phi^4 theory in 3+1 dimensions
• Functional renormalisation group approach to far-from-equilibrium quantum field dynamics
• 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
• Systematic approach to leptogenesis in nonequilibrium QFT: self-energy contribution to the CP-violating parameter
• Two-loop HTL Thermodynamics with Quarks
• Renormalizability of Phi-derivable approximations in scalar phi^4 theory
• 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
• 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
• Symmetry Improved CJT Effective Action
• Four-loop screened perturbation theory
• Transport coefficients from the 2PI effective action
• Gapless Hartree-Fock Resummation Scheme for the O(N) Model
• Comparison of Boltzmann Equations with Quantum Dynamics for Scalar Fields
• Renormalization group methods and the 2PI effective action
• Quantum field thermalization in expanding backgrounds
• 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
• Deriving Boltzmann Equations from Kadanoff-Baym Equations in Curved Space-Time
• 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
• Exact renormalization group and Phi-derivable approximations
• Constraining the effective action by a method of external sources
• Renormalization group approach to interacting fermion systems in the two-particle-irreducible formalism
• The Quark-Mass Dependence of T_C in QCD: Working up from m=0 or down from m=infinity ?
• 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 O(N) linear sigma model at finite temperature beyond the Hartree approximation
• 2PI effective action for gauge theories: Renormalization
• The 2PI effective theory at next-to-leading order using the functional renormalization group
• Symmetry-Improved 2PI Approach to the Goldstone-Boson IR Problem of the SM Effective Potential
• 2PI functional techniques for gauge theories: QED
• Thermalization of an Interacting Quantum Field in the CTP-2PI Next-to-leading-order Large N Scheme
• Resummed one-loop determination of the phase boundary of the SU(3)_R x SU(3)_L linear sigma model in the m_pi-m_K-plane
• Renormalised nonequilibrium quantum field theory: scalar fields
• 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
• Progress in nonequilibrium quantum field theory III
• The 2PI effective action at four loop order in ${\phi }^4$ theory
• Self-consistent description of vector-mesons in matter
• Three-loop Phi-derivable Approximation in QED
• Renormalization of a gapless Hartree-Fock approximation to a theory with spontaneously broken O(N)-symmetry
• Next-to-Leading Order Transport Coefficients from the Four-Particle Irreducible Effective Action
• Symmetry Improved 2PI Effective Action and the Infrared Divergences of the Standard Model
• Renormalization group flow equations connected to the $n$PI effective action
• Broken phase scalar effective potential and Phi-derivable approximations
• Ward Identities for the 2PI effective action in QED
• Renormalization group and nonequilibrium action in stochastic field theory
• The pressure of QED from the two-loop 2PI effective action
• Non-equilibrium dynamics of a scalar field with quantum backreaction
• Nonperturbative renormalization of Phi-derivable approximations in theories with fermions
• Out-of-equilibrium electromagnetic radiation
• Some Aspects of the Theory of Heavy Ion Collisions
• Non-perturbative finite $T$ broadening of the $\rho$ meson and dilepton emission in heavy ion-collisions
• Effective convergence of the 2PI-1/N expansion for nonequilibrium quantum fields
• Renormalized effective actions for the O(N) model at next-to-leading order of the 1/N expansion
• Selfconsistent approximations, symmetries and choice of representation
• Entropy production in 2D $\lambda {\varphi }^4$ theory in the Kadanoff-Baym approach
• Thermal effects on slow-roll dynamics
• Bethe-Salpeter Equations from the 4PI effective action
• Effects of Renormalizing the chiral SU(2) Quark-Meson-Model
• Role reversal in first and second sound in a relativistic superfluid
• Counterterm resummation for 2PI-approximation in constant background
• Exact RG Invariance and Symmetry Improved 2PI Effective Potential
• Hadron Liquid with a Small Baryon Chemical Potential at Finite Temperature
• 4-point vertices from the 2PI and 4PI Effective Actions
• Non-equilibrium quantum mechanics: A 'hot quantum soup' of paramagnons
• The Gross-Neveu model at finite temperature at next to leading order in the 1/N expansion
• Study of chiral symmetry restoration in linear and nonlinear O(N) models using the auxiliary field method
• Renormalization of O(N) model in 1/N expansion in auxiliary field formalism
• 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
• A new method to calculate the n-Particle Irreducible Effective Action
• Single-particle spectral function for the classical one-component plasma
• Two-loop HTL-resummed thermodynamics for N=4 supersymmetric Yang-Mills theory
• Renormalization of the 4PI effective action using the functional renormalization group
• A critical look at the role of the bare parameters in the renormalization of Phi-derivable approximations
• The effect of memory on relaxation in a scalar field theory
• The absence of Ginzburg-Landau mechanism for vestigial order in the normal phase above a two-component superconductor
• 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 group flow equations with full momentum dependence
• Renormalization in momentum dependent resummations
• Renormalization of pionless effective field theory in the A-body sector
• 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
• 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
• Dynamics of Resonances in Strongly Interacting Systems
• Kinetics of the chiral phase transition in a quark-meson $\sigma$-model
• Non-perturbative construction of counterterms for 2PI-approximation
• Non-perturbative renormalization of Phi-derivable approximations in theories with multiple fields
• 2PI renormalized effective action for gauge theories
• Zero point energy of composite particles: The medium effects
• 2PI functional techniques for abelian gauge theories
• Non-Equilibrium 2PI Potential and Its Possible Application to Evaluation of Bulk Viscosity
• A new resummation scheme in scalar field theories
• Selfconsistent descriptions of vector-mesons in hot matter revisited
• Field theoretical approach to spin models
• Infrared Behavior of the Pressure in $g{\varphi }^3$ Theory Reexamined