We observe that probing certain classical field theories by external sources uncovers the underlying renormalization group structure, including the phenomenon of dimensional transmutation, at purely-classical level. We perform this study on an example of λψ4 theory and unravel asymptotic freedom and triviality for negative and positives signs of λ respectively We derive exact classical β function equation. Solving this equation we find that an isolated source has an infinite energy and therefore cannot exist as an asymptotic state. On the other hand a dipole, built out of two opposite charges, has finite positive energy. At large separation the interaction potential between these two charges grows indefinitely as a distance in power one third.
- Asymptotic freedom
- Renormalization group
- Renormalization regularization and renormalons
ASJC Scopus subject areas
- Nuclear and High Energy Physics