Renormalization in momentum dependent resummations

Abstract

At finite temperature and in non-equilibrium environments we have to resum perturbation theory to avoid infrared divergences. Since resummation shuffles the perturbative orders, renormalizability is a nontrivial issue. In this paper we demonstrate that one can modify any type of resummations -- even if it is momentum dependent, or it resums higher point functions -- in a way that it is renormalizable with the usual zero temperature counterterms. To achieve this goal we reformulate resummation in form of a renormalization scheme. We apply this technique to perform a 2PI resummation in the six dimensional cubic scalar model in equilibrium.

16 pages revtex4, 4 figures included; typos corrected, references added

References in corpus (24)

• Resummation in a Hot Scalar Field Theory
• Screened Perturbation Theory
• Controlled nonperturbative dynamics of quantum fields out of equilibrium
• Parametric resonance in quantum field theory
• Thermalization of Quantum Fields from Time-Reversal Invariant Evolution Equations
• Classical aspects of quantum fields far from equilibrium
• Nonperturbative renormalization for 2PI effective action techniques
• Renormalization in Self-Consistent Approximations schemes at Finite Temperature I: Theory
• Nonequilibrium time evolution of the spectral function in quantum field theory
• 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
• The weak electroweak phase transition
• On the nature of the electroweak phase transition
• Renormalization of Φ-derivable approximations in scalar field theories
• Equilibration in phi^4 theory in 3+1 dimensions
• Renormalizability of Phi-derivable approximations in scalar phi^4 theory
• Renormalizing the Schwinger-Dyson equations in the auxiliary field formulation of $\lambda {\varphi }^4$ field theory
• Environmentally Friendly Renormalization
• Nonperturbative calculation of the shear viscosity in hot phi**4 theory in real time
• The Chiral Fermion Meson Model at Finite Temperature
• Ultraviolet cascade in the thermalization of the classical phi^4 theory in 3+1 dimensions
• Summation and renormalization of bubble graphs to all orders
• Renormalization and resummation in finite temperature field theories
• The renormalized and Renormalization-Group invariant Hartree-Fock approximation

Cited by in corpus (7)

• Renormalisability of the 2PI-Hartree approximation of multicomponent scalar models in the broken symmetry phase
• Renormalised nonequilibrium quantum field theory: scalar fields
• 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
• Broken symmetry phase solution of the phi^4 model at two-loop level of the Phi-derivable approximation
• Renormalization and resummation in the O(N) model