Abstract
We use the scalar model with quartic interaction to illustrate how a nonperturbative variational technique combined with renormalization group (RG) properties efficiently resums perturbative expansions in thermal field theories. The resulting convergence and scale dependence of optimized thermodynamical quantities, here illustrated up to two-loop order, are drastically improved as compared to standard perturbative expansions, as well as to other related methods such as the screened perturbation or (resummed) hard-thermal-loop perturbation, that miss RG invariance (as we explain). Being very general and easy to implement, our method is a potential analytical alternative to dealing with the phase transitions of field theories such as thermal QCD.
Highlights
We use the scalar model with quartic interaction to illustrate how a nonperturbative variational technique combined with renormalization group (RG) properties efficiently resums perturbative expansions in thermal field theories
At sufficiently high temperature or density, one could naively hope that the asymptotic freedom property of quantum chromodynamics (QCD) would give a reliable perturbation theory (PT) handle on the quark-gluon plasma physics
lattice field theory (LFT) has been very successful in the description of the QCD phase transitions at finite temperatures and near vanishing baryonic densities, with results [2] which can be directly used for interpreting the experimental output from heavy ion experiments envisaged to scan over this particular region of the phase diagram
Summary
We use the scalar model with quartic interaction to illustrate how a nonperturbative variational technique combined with renormalization group (RG) properties efficiently resums perturbative expansions in thermal field theories. We claim it largely explains the degrading scale-dependence at higher orders in other similar resummation methods like SPT and HTLpt, which ignore those finite vacuum energy terms.
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