Classical Dimensional Transmutation and Confinement

Details Classical Dimensional Transmutation and Confinement Classical Dimensional Transmutation and Confinement

2011-07-05

arxiv.org/abs/1107.0870v1

Physics

High Energy Physics

High Energy Physics - Theory

Scientific paper

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 $\lambda\phi^{4}$ theory and unravel asymptotic freedom and triviality for negative and positives signs of $\lambda$ respectively. We derive exact classical $\beta$ 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.

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