Renormalizing the Schwinger-Dyson equations in the auxiliary field formulation of $\lambda {\varphi }^4$ field theory

Abstract

In this paper we study the renormalization of the Schwinger-Dyson equations that arise in the auxiliary field formulation of the O(N) ${\varphi }^4$ field theory. The auxiliary field formulation allows a simple interpretation of the large-N expansion as a loop expansion of the generating functional in the auxiliary field $\chi$, once the effective action is obtained by integrating over the $\varphi$ fields. Our all orders result is then used to obtain finite renormalized Schwinger-Dyson equations based on truncation expansions which utilize the two-particle irreducible (2-PI) generating function formalism. We first do an all orders renormalization of the two- and three-point function equations in the vacuum sector. This result is then used to obtain explicitly finite and renormalization constant independent self-consistent S-D equations valid to order~1/N, in both 2+1 and 3+1 dimensions. We compare the results for the real and imaginary parts of the renormalized Green's functions with the related \emph{sunset} approximation to the 2-PI equations discussed by Van Hees and Knoll, and comment on the importance of the Landau pole effect.

20 pages, 10 figures

References in corpus (31)

• Controlled nonperturbative dynamics of quantum fields out of equilibrium
• Non-Equilibrium Quantum Fields in the Large N Expansion
• The entropy of the QCD plasma
• Far-from-equilibrium dynamics with broken symmetries from the 2PI-1/N expansion
• Parametric resonance in quantum field theory
• Thermalization of Quantum Fields from Time-Reversal Invariant Evolution Equations
• Classical aspects of quantum fields far from equilibrium
• Advances in perturbative thermal field theory
• Renormalization in Self-Consistent Approximations schemes at Finite Temperature I: Theory
• Quantum dynamics and thermalization for out-of-equilibrium phi^4-theory
• Thermalization of fermionic quantum fields
• Nonequilibrium time evolution of the spectral function in quantum field theory
• Nonequilibrium Quantum Dynamics Of Disoriented Chiral Condensates
• 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
• Shear Viscosity in the O(N) Model
• Time evolution of the chiral phase transition during a spherical expansion
• Renormalizability of Phi-derivable approximations in scalar phi^4 theory
• Quantum dynamics of phase transitions in broken symmetry $\lambda {\varphi }^4$ field theory
• Schwinger-Dyson approach to non-equilibrium classical field theory
• Resumming the large-N approximation for time evolving quantum systems
• Transport coefficients from the 2PI effective action
• Time evolution of correlation functions in Non-equilibrium Field Theories
• Exact and approximate dynamics of the quantum mechanical O(N) model
• Order 1/N corrections to the time-dependent Hartree approximation for a system of N+1 oscillators
• Dynamics of broken symmetry lambda phi^4 field theory
• Nonequilibrium evolution of Phi**4 theory in 1+1 dimensions in the 2PPI formalism
• Out-of-equilibrium evolution of quantum fields in the hybrid model with quantum back reaction
• Hydrodynamic scaling from the dynamics of relativistic quantum field theory
• Real-time dynamics of the O(N) model in 1+1 dimensions
• Quantum dynamics of Phi**4 field theory beyond leading order in 1+1 dimensions

Cited by in corpus (36)

• Aspects of the Functional Renormalisation Group
• Nonperturbative renormalization for 2PI effective action techniques
• Equilibration in phi^4 theory in 3+1 dimensions
• Renormalized thermodynamics from the 2PI effective action
• Transport coefficients in large N_f gauge theories with massive fermions
• Exact renormalization group and Phi-derivable approximations
• Isotropization far from equilibrium
• 2PI effective action for gauge theories: Renormalization
• 2PI functional techniques for gauge theories: QED
• Symmetry and Mass Degeneration in Multi-Higgs-Doublet Models
• Physical momentum representation of scalar field correlators in de Sitter space
• Progress in nonequilibrium quantum field theory III
• Renormalized broken-symmetry Schwinger-Dyson equations and the 2PI-1/N expansion for the O(N) model
• Renormalization of a gapless Hartree-Fock approximation to a theory with spontaneously broken O(N)-symmetry
• On the Question of an Ultraviolet Zero of the Beta Function of the $\lambda ({\vec{\varphi }}^2{)}_4^2$ Theory
• Ward Identities for the 2PI effective action in QED
• Nonperturbative renormalization of Phi-derivable approximations in theories with fermions
• Implications of analyticity to solution of Schwinger-Dyson equations in Minkowski space
• 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
• Quasi-diagonal Inhomogeneous Closure for Classical and Quantum Statistical Dynamics
• Counterterm resummation for 2PI-approximation in constant background
• Renormalization of O(N) model in 1/N expansion in auxiliary field formalism
• Renormalization of 2PI resummation: a renormalization scheme approach
• Padé approximants and analytic continuation of Euclidean Phi-derivable approximations
• The renormalized and Renormalization-Group invariant Hartree-Fock approximation
• Mean-field description of pairing effects, BKT physics, and superfluidity in 2D Bose gases
• Renormalization in momentum dependent resummations
• Addressing energy density functionals in the language of path-integrals I: Comparative study of diagrammatic techniques applied to the (0+0)-D $O(N)$-symmetric ${\phi }^4$-theory
• Broken symmetry phase solution of the phi^4 model at two-loop level of the Phi-derivable approximation
• Spontaneous symmetry breakings in the singlet scalar Yukawa model within the auxiliary field method
• On aspects of self-consistency in the Dyson-Schwinger approach to QED and λ(ϕ^\star ϕ)^2 theories
• Simulations in Early Universe Theory
• 2PI renormalized effective action for gauge theories
• 2PI functional techniques for abelian gauge theories
• Improved Hartree--Fock resummations and spontaneous symmetry breaking