On asymptotically free scalar fields

Abstract: I present recent work (Annales Henri Poincaré 2022) analysing the flow equations of the renormalisation group in the mean field approximation. There it is shown that these equations for scalar fields in four dimensional euclidean space, have solutions which are UV asymptotically free. I comment on this result, also in view of the literature, in particular with regard to the triviality of \varphi^4_4-theory. We close with an outlook on future perspectives.

mathematical physics

Audience: researchers in the discipline

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