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Classical dimensional transmutation and confinement
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DOI：10.1007/JHEP12(2011)103.png)
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Abstract
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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.
Keywords:
Asymptotic Freedom
Renormalization Group
Renormalization Regularization and Renormalons
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5.5
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4.0W
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13.7W
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