Summary
The two-loop order effective potential is calculated for the (γϕ4)2 theory, using two different techniques: the functional formalism and the so-called tadpole method. These procedures are applied to the three possible cases for the mass, namelym 2>0,m 2<0, andm 2=0. The convexity properties are particularly analysed, both when they are already present in the classical case, and also when their origin lies in the quantum contribution.
Riassunto
Si calcola il potenziale efficace di ordine a due loop per la teoria (γϕ4)2, usando due diverse techniche: il formalismo funzionale e il cosidetto metodo del tadpole. Questi procedimenti sono applicati a tre possibili casi per la massa, cioèm 2>0,m 2<0 em 2=0. Si analizzano in particolare le proprietà di convessità, sia quando sono già presenti nel caso classico, sia quando si originano nel contributo quantistico.
Резюме
Вычисляется двух-петельный эффективный потенциал для теории (γϕ4)2, используя два различных подхода: функциональный формалиам и так называемый “головастиковый” детод. Используются три возможные случая для массы, а именноm 2>0,m 2<0 иm 2=0. Анализируются свойства выпуклости, когда они уже присутствуют в классическом случае и когда они обусловлены квантовым происхождением.
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Boya, L.J., Casahorran, J. Two-loop effective potential in (γϕ4)2 . Nuov Cim A 100, 907–918 (1988). https://doi.org/10.1007/BF02789009
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DOI: https://doi.org/10.1007/BF02789009