Kurt Symanzik - a stable fixed point beyond triviality

TL;DR

This paper revisits Symanzik's 1970 proposal of a non-Hermitian phi^4-theory with negative coupling, arguing it may represent a stable, non-trivial fixed point beyond triviality, challenging conventional views.

Contribution

It provides a historical and formal analysis of Symanzik's non-Hermitian phi^4-theory, suggesting it could be a valid asymptotically free and stable fixed point.

Findings

Re-examination of Symanzik's theory in a modern context

Challenging the view that non-Hermitian theories are unstable

Proposing the theory as a candidate for a non-trivial fixed point

Abstract

In 1970 Kurt Symanzik proposed a "precarious" phi**4-theory with a negative quartic coupling constant as a valid candidate for an asymptotically free theory of strong interactions. Symanzik's deep insight in the non-trivial properties of this theory has been overruled since then by the Hermitian intuition of generations of scientists, who considered or consider this actually non-Hermitian highly important theory to be unstable. This short - certainly controversial - communication tries to shed some light on the historical and formalistic context of Symanzik's theory in order to sharpen our (quantum) intuition about non-perturbative theoretical physics between (non)triviality and asymptotic freedom.