On (non-Hermitian) Lagrangeans in (particle) physics and their dynamical generation

Abstract

On the basis of a new method to derive the effective action the nonperturbative concept of "dynamical generation" is explained. A non-trivial, non-Hermitian and PT-symmetric solution for Wightman's scalar field theory in four dimensions is dynamically generated, rehabilitating Symanzik's precarious phi**4-theory with a negative quartic coupling constant as a candidate for an asymptotically free theory of strong interactions. Finally it is shown making use of dynamically generation that a Symanzik-like field theory with scalar confinement for the theory of strong interactions can be even suggested by experiment.