ABSTRACT
The considerations about spontaneous symmetry breaking up to now are based on the classical potential introduced in (18.3). The quantum effects of the potential can be calculated by an expansion in powers of Planck’s constant, ħ $ \hbar $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315369723/48d43afe-85b0-4e2b-a932-df2bd1af07be/content/inline-math20_2013.tif"/> , starting from the functional methods introduced originally by Schwinger [43], applied to spontaneous symmetry breaking by Jona–Lasinio and other authors [44,45], and more recently by Coleman and Weinberg [28] in the context of the Standard Theory. For an extended review, see [46]. 1 After analysing the ultraviolet divergences which characterise the effective potential, we illustrate the conceptual difficulties which arise from the presence of elementary scalar fields in a renormalisable field theory.
