The 2PI effective action at four loop order in ${\phi }^4$ theory

Abstract

It is well known that perturbative pressure calculations show poor convergence. Calculations using a two particle irreducible (2PI) effective action show improved convergence at the 3 loop level, but no calculations have been done at 4 loops. We consider the 2PI effective theory for a symmetric scalar theory with quartic coupling in 4-dimensions. We calculate the pressure and two different non-perturbative vertices as functions of coupling and temperature. Our results show that the 4 loop contribution can become larger than the 3 loop term when the coupling is large. This indicates a breakdown of the 2PI approach, and the need for higher order $n$PI approximations. In addition, our results demonstrate the renormalizability of 2PI calculations at the 4 loop level. This is interesting because the counterterm structure of the 2PI theory at 4 loops is different from the structure at $n\le 3$ loops. Two vertex counterterms are required at the 4 loop level, but not at lower loop order. This unique feature of the 2PI theory has not previously been verified numerically.

15 pages, 6 figures

References in corpus (12)

• Three-loop hard-thermal-loop perturbation theory thermodynamics at finite temperature and finite baryonic and isospin chemical potential
• Four-loop screened perturbation theory
• Renormalization group methods and the 2PI effective action
• Symmetry-Improved 2PI Approach to the Goldstone-Boson IR Problem of the SM Effective Potential
• Renormalisability of the 2PI-Hartree approximation of multicomponent scalar models in the broken symmetry phase
• Nonequilibrium dynamics in the O(N) model to next-to-next-to-leading order in the 1/N expansion
• QED Electrical Conductivity using the 2PI Effective Action
• Leading Order QED Electrical Conductivity from the 3PI Effective Action
• The pressure of QED from the two-loop 2PI effective action
• The O(N)-model within the Phi-derivable expansion to order lambda^2: on the existence, UV and IR sensitivity of the solutions to self-consistent equations
• Effective convergence of the 2PI-1/N expansion for nonequilibrium quantum fields
• Validating the 2PI resummation: the Bloch-Nordsieck example

Cited by in corpus (5)

• The nonperturbative functional renormalization group and its applications
• The 2PI effective theory at next-to-leading order using the functional renormalization group
• Renormalization of the 4PI effective action using the functional renormalization group
• Renormalization group optimized $\lambda {\varphi }^4$ pressure at next-to-next-to-leading order
• Schwinger-Keldysh non-perturbative field theory of open quantum systems beyond the Markovian regime: Application to spin-boson and spin-chain-boson models