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

TL;DR

This paper introduces a new method for deriving effective actions, demonstrating the dynamical generation of a non-Hermitian, PT-symmetric scalar field theory that could model strong interactions and scalar confinement.

Contribution

It presents a novel approach to effective action derivation and shows how non-Hermitian, PT-symmetric solutions can be dynamically generated in scalar field theories, suggesting new models for strong interactions.

Findings

Dynamically generated non-Hermitian PT-symmetric scalar field solution in four dimensions.

Rehabilitation of Symanzik's phi^4-theory with negative coupling as asymptotically free.

Proposal of a scalar confinement model consistent with experimental indications.

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.