Asymptotic Freedom in QCD



From the Bjorken scaling of the nucleon structure functions, we learn that the hadronic constituents probed at small distance or at high energy behave as if they were almost noninteracting or ‘free’. We are confronted with an apparent paradox, since in quantum field theory virtual particles exchanged between partons can have arbitrarily high momenta, quantum fluctuations associated with them naturally occur at short distances. Why do these fluctuations turn themselves off, and the partons behave as if they were free at high energy, whereas at low energy they are strongly bound? How can a model of noninteracting quarks be reconciled with a force that is extremely strong in other circumstances?


Renormalization Group Feynman Rule Vacuum Polarization Renormalization Group Equation Vertex Function 
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Suggestions for Further Reading

Field Theory, Renormalization

  1. Collins, J. C., Renormalization Cambridge U. Press, Cambridge 1984zbMATHCrossRefGoogle Scholar
  2. Hatfield, B., Quantum Field Theory of Point Particles and Strings. Addison-Wesley, Redwood, CA 1992zbMATHGoogle Scholar
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Quantization of Yang—Mills fields

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Vacuum polarization 111’(q), vertex function I’’(p, p), fermionic self-energy E(p)

  1. De Wit, B. and Smith, J., Field Theory in Particle Physics (Vol. I ). North-Holland, Amsterdam 1986Google Scholar
  2. Peskin, M. E. and Schroeder, D. V., An Introduction to Quantum Field Theory. Addison-Wesley, Reading, MA 1995Google Scholar

Renormalization group method and 13-functions

  1. Cheng, Ta-Pei and Li, Ling-Fong, Gauge Theory of Elementary Particle Physics. Oxford U. Press, New York 1984Google Scholar

Peskin, M. E. and Schroeder, D. V., (op. cit.)

  1. Weinberg, S., The Quantum Theory of Fields (Vol. II.) Cambridge U. Press, Cambridge 1996Google Scholar

Ghosts and unitarity, Cancelation of gauge-dependent 1 terms

  1. Aitchison, I. J. R. and Hey, A. J. G., Gauge Theories in Particle Physics ( Second edition ). Adam Hilger, Bristol 1989zbMATHCrossRefGoogle Scholar
  2. Feng, Y. J. and Lam, C. S., Phys. Rev. D53 (1996) 2115Google Scholar
  3. Gross, F., Relativistic Quantum Mechanics and Field Theory. Wiley-Interscience, New York 1993Google Scholar

Perturbative QCD, GLAP equations

  1. Field, R. D., Applications of Perturbative QCD. Addison-Wesley, Redwood, CA 1989Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  1. 1.Physics DepartmentUniversité LavalSte-FoyCanada
  2. 2.Laboratoire de Physique Théorique et Hautes EnergiesUniversités Paris VI et VIIParis Cedex 05France

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