The renormalized and Renormalization-Group invariant Hartree-Fock approximation

Abstract

We study the renormalization problem for the Hartree--Fock approximation of the $O(N)-$invariant ${\varphi }^4$ model in the symmetric phase and show how to systematically improve the corresponding diagrammatic resummation to achieve the correct renormalization properties of the effective field equations, including Renormalization--Group invariance with the one--loop beta function. These new Hartree--Fock dynamics is still of mean field type but includes memory effects which are generically nonlocal also in space.

arXiv comment32 pages, 13 figures

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Cited by in corpus (9)

• Renormalisability of the 2PI-Hartree approximation of multicomponent scalar models in the broken symmetry phase
• Broken phase scalar effective potential and Phi-derivable approximations
• 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
• Renormalization of O(N) model in 1/N expansion in auxiliary field formalism
• Renormalization of 2PI resummation: a renormalization scheme approach
• Kinetic theory and classical limit for real scalar quantum field in curved space-time
• Machian Classical and Semiclassical Emergent Time
• Renormalization in momentum dependent resummations
• Improved Hartree--Fock resummations and spontaneous symmetry breaking