Renormalization of self-consistent $Φ$-derivable approximations

H. van Hees; J. Knoll

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arXiv · hep-ph/0210262

Renormalization of self-consistent $Φ$-derivable approximations

H. van Hees·J. Knoll

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Abstract

Within finite temperature field theory, we show that truncated non-perturbative self-consistent Dyson resummation schemes can be renormalized with local vacuum counterterms. For this the theory has to be renormalizable in the usual sense and the self-consistent scheme must follow Baym's Phi-derivable concept. Our BPHZ-renormalization scheme leads to renormalized self-consistent equations of motion. At the same time the corresponding 2PI-generating functional and the thermodynamic potential can be renormalized with the same counterterms used for the equations of motion. This guarantees the standard Phi-derivable properties like thermodynamic consistency and exact conservation laws also for the renormalized approximation schemes. We give also a short overview over symmetry properties of the various functions defined within the 2PI scheme for the case that the underlying classical field theory has a global linearly realized symmetry.

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H. van Hees, J. Knoll. 2002-11-04. Renormalization of self-consistent $Φ$-derivable approximations. https://arxiv.org/abs/hep-ph/0210262

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