Renormalization Group and Strong Interactions

Kenneth G. Wilson
Phys. Rev. D 3, 1818 – Published 15 April 1971
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Abstract

The renormalization-group method of Gell-Mann and Low is applied to field theories of strong interactions. It is assumed that renormalization-group equations exist for strong interactions which involve one or several momentum-dependent coupling constants. The further assumption that these coupling constants approach fixed values as the momentum goes to infinity is discussed in detail. However, an alternative is suggested, namely, that these coupling constants approach a limit cycle in the limit of large momenta. Some results of this paper are: (1) The e+e annihilation experiments above 1-GeV energy may distinguish a fixed point from a limit cycle or other asymptotic behavior. (2) If electrodynamics or weak interactions become strong above some large momentum Λ, then the renormalization group can be used (in principle) to determine the renormalized coupling constants of strong interactions, except for U(3)×U(3) symmetry-breaking parameters. (3) Mass terms in the Lagrangian of strong, weak, and electromagnetic interactions must break a symmetry of the combined interactions with zero mass. (4) The ΔI=12 rule in nonleptonic weak interactions can be understood assuming only that a renormalization group exists for strong interactions.

  • Received 30 November 1970

DOI:https://doi.org/10.1103/PhysRevD.3.1818

©1971 American Physical Society

Authors & Affiliations

Kenneth G. Wilson*

  • Stanford Linear Accelerator Center, Stanford University, Stanford, California 94305
  • Laboratory of Nuclear Studies, Cornell University, Ithaca, New York 14850

  • *Present and permanent address.

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Vol. 3, Iss. 8 — 15 April 1971

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