%0 Journal Article %1 Fujimoto1983268 %A Fujimoto, Y. %A O'Raifeartaigh, L. %A Parravicini, G. %D 1983 %J Nuclear Physics B %K LoopExpansion NonconvexPotential OneLoop OneLoopEffectivePotential Supersymmetry WessZuminoModel %N 2 %P 268 - 300 %R DOI: 10.1016/0550-3213(83)90305-X %T Effective potential for non-convex potentials %U http://www.sciencedirect.com/science/article/B6TVC-471YW0B-1G8/2/bf1f9ac9b8b6ea9f1038560961175709 %V 212 %X It is shown that the well-known relationship between the effective potential Gamma and the vacuum graphs Sigma of scalar QFT follows directly from the translational invariance of the measure, and that it holds for all values of the fields phi if, and only if, the classical potential is convex. In the non-convex case Sigma appears to become complex for some values of phi, but it is shown that the complexity is only apparent and is due to the failure of the loop expansion. The effective potential actually remains real and well-defined for all phi, and reduces to Sigma in the neighbourhood of the classical minima. A number of examples are considered, notably potentials which are spontaneously broken. In particular the mechanism by which a spontaneous breakdown may be generated by radiative corrections is re-investigated and some new insights obtained. Finally, it is shown that the renormalization group equations for the parameters may be obtained by inspection from the effective potential, and among the examples considered are SU(n) fields and supermultiplets. In particular, it is shown that for supermultiplets the effective potential is not only real but positive.

@article{Fujimoto1983268, abstract = {It is shown that the well-known relationship between the effective potential [Gamma] and the vacuum graphs [Sigma] of scalar QFT follows directly from the translational invariance of the measure, and that it holds for all values of the fields [phi] if, and only if, the classical potential is convex. In the non-convex case [Sigma] appears to become complex for some values of [phi], but it is shown that the complexity is only apparent and is due to the failure of the loop expansion. The effective potential actually remains real and well-defined for all [phi], and reduces to [Sigma] in the neighbourhood of the classical minima. A number of examples are considered, notably potentials which are spontaneously broken. In particular the mechanism by which a spontaneous breakdown may be generated by radiative corrections is re-investigated and some new insights obtained. Finally, it is shown that the renormalization group equations for the parameters may be obtained by inspection from the effective potential, and among the examples considered are SU(n) fields and supermultiplets. In particular, it is shown that for supermultiplets the effective potential is not only real but positive.}, added-at = {2009-04-16T17:29:31.000+0200}, author = {Fujimoto, Y. and O'Raifeartaigh, L. and Parravicini, G.}, biburl = {https://www.bibsonomy.org/bibtex/297b391fa253db56aedae9058dd017829/gber}, description = {ScienceDirect - Nuclear Physics B : Effective potential for non-convex potentials}, doi = {DOI: 10.1016/0550-3213(83)90305-X}, interhash = {b992aa41cd125a1910cd589013148b35}, intrahash = {97b391fa253db56aedae9058dd017829}, issn = {0550-3213}, journal = {Nuclear Physics B}, keywords = {LoopExpansion NonconvexPotential OneLoop OneLoopEffectivePotential Supersymmetry WessZuminoModel}, number = 2, pages = {268 - 300}, timestamp = {2009-04-16T17:29:31.000+0200}, title = {Effective potential for non-convex potentials}, url = {http://www.sciencedirect.com/science/article/B6TVC-471YW0B-1G8/2/bf1f9ac9b8b6ea9f1038560961175709}, volume = 212, year = 1983 }