Renormalization of self-consistent $\Phi$-derivable approximations
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.
Cite
@article{arxiv.hep-ph/0210262,
title = {Renormalization of self-consistent $\Phi$-derivable approximations},
author = {H. van Hees and J. Knoll},
journal= {arXiv preprint arXiv:hep-ph/0210262},
year = {2007}
}
Comments
16 pages, LaTeX using ws-procs9x6.cls (included)<br> To appear in the proceedings of the workshop "Progress in Nonequilibrium Greens Functions, Dresden, Germany, 19.-22. August 2002" 2nd Version: Added a section "Conclusions and outlooks" (physics contents unchanged)