Kurt Symanzik - a stable fixed point beyond triviality

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.

6 pages, no figures, new style files, revised for typos, improved discussion, new references added

References in corpus (10)

• Introduction to PT-Symmetric Quantum Theory
• Physical Aspects of Pseudo-Hermitian and $PT$-Symmetric Quantum Mechanics
• Spectra of PT-Symmetric Operators and Perturbation Theory
• The Origins of Lattice Gauge Theory
• PT-Symmetric Quantum Electrodynamics
• The C Operator in PT-Symmetric Quantum Field Theory Transforms as a Lorentz Scalar
• Beyond the WKB approximation in PT-symmetric quantum mechanics
• Lattice gluodynamics at negative g^2
• On (non-Hermitian) Lagrangeans in (particle) physics and their dynamical generation
• Historical curiosity: how asymptotic freedom of the Yang-Mills theory could have been discovered three times before Gross, Wilczek, and Politzer, but was not

Cited by in corpus (11)

• Making Sense of Non-Hermitian Hamiltonians
• Equivalence of a Complex $\cP\cT$-Symmetric Quartic Hamiltonian and a Hermitian Quartic Hamiltonian with an Anomaly
• General Aspects of PT-Symmetric and P-Self-Adjoint Quantum Theory in a Krein Space
• Non-perturbative tests for the Asymptotic Freedom in the $\mathcal{P}\mathcal{T}$-symmetric $(-{\varphi }^4{)}_{3+1}$ theory
• Extrapolating the precision of the Hypergeometric Resummation to Strong couplings with application to the $\mathcal{P}\mathcal{T}-$Symmetric $i{\varphi }^3$ Field Theory
• On some meaningful inner product for real Klein-Gordon fields with positive semi-definite norm
• Asymptotic behavior in a model with Yukawa interaction from Schwinger-Dyson equations
• Isomorphic Hilbert spaces associated with different Complex Contours of the $\mathcal{P}\mathcal{T}$-Symmetric $(-x^4)$ Theory
• Representation Dependence of Superficial Degree of Divergences in Quantum Field Theory
• Identification of the metric for diagonalizable (anti-)pseudo-Hermitian Hamilton operators represented by two-dimensional matrices
• Vacuum Stability of the wrong sign $(-{\varphi }^6)$ Scalar Field Theory