Threeloop contributions to the free energy of $\lambda\varphi^4$ QFT
Abstract
The massive scalar field with $\lambda\varphi^4$ interaction placed in $(3+1)$ dimensional box is considered. The sizes of the box are $V\times \beta$ $(V=L^3$ is the volume, $T=1/\beta$ is the temperature). The free energy is evaluated up to the 2nd order of $PT$. The averaging on the vacuum fluctuations is separated from the averaging on the thermal fluctuations explicitly. As result the freeenergy is expressed through the scattering amplitudes. We find that in 3loop approximation the expression for free energy coincides with the ansatz of Bernstein, Dashen, Ma suggested on the base of $S$matrix formulation of statistical mechanics. The obtained expressions are generalized for higher order of $PT$.
 Publication:

arXiv eprints
 Pub Date:
 October 1995
 arXiv:
 arXiv:hepth/9510232
 Bibcode:
 1995hep.th...10232B
 Keywords:

 High Energy Physics  Theory
 EPrint:
 11 pages, LaTeX file