Английская Википедия:Dimensional transmutation
Шаблон:Short description Шаблон:More citations needed In particle physics, dimensional transmutation is a physical mechanism providing a linkage between a dimensionless parameter and a dimensionful parameter.[1]
In classical field theory, such as gauge theory in four-dimensional spacetime, the coupling constant is a dimensionless constant. However, upon quantization, logarithmic divergences in one-loop diagrams of perturbation theory imply that this "constant" actually depends on the typical energy scale of the processes under considerations, called the renormalization group (RG) scale. This "running" of the coupling is specified by the beta-function of the renormalization group.
Consequently, the interaction may be characterised by a dimensionful parameter Шаблон:Mvar, namely the value of the RG scale at which the coupling constant diverges. In the case of quantum chromodynamics, this energy scale Шаблон:Mvar is called the QCD scale, and its value 220 MeV supplants the role of the original dimensionless coupling constant in the form of the logarithm (at one-loop) of the ratio Шаблон:Math and Шаблон:Math. Perturbation theory, which produced this type of running formula, is only valid for a (dimensionless) coupling Шаблон:Mvar ≪ 1. In the case of QCD, the energy scale Шаблон:Mvar is an infrared cutoff, such that Шаблон:Math implies Шаблон:Math, with Шаблон:Mvar the RG scale.
On the other hand, in the case of theories such as QED, Шаблон:Mvar is an ultraviolet cutoff, such that Шаблон:Math implies Шаблон:Math.
This is also a way of saying that the conformal symmetry of the classical theory is anomalously broken upon quantization, thereby setting up a mass scale. See conformal anomaly.
References
Шаблон:Reflist Шаблон:Quantum-stub
- ↑ Cao, Tian Yu. From Current Algebra to Quantum Chromodynamics: A Case for Structural Realism. Cambridge University Press, 2010. 163.
