On 't Hooft's representation of the β-function

Abstract

It is demonstrated, that 't Hooft's renormalization scheme (in which β-function has exactly the two-loop form) is generally in conflict with the natural physical requirements and specifies the type of the field theory in an arbitrary manner. It violates analytic properties in the coupling constant plane and provokes misleading conclusion on accumulation of singularities near the origin. It artificially creates renormalon singularities, even if they are absent in the physical scheme. The 't Hooft scheme can be used in the framework of perturbation theory but no global conclusions should be drawn from it.