Infra-Red Behavior of the Running Coupling Constant in QCD

  • James S. Ball
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 55)


In these lectures I will describe a non-perturbative method of studying the infrared (IR) structure of Quantum Chromodynamics (QCD) [1] and then follow with the description of an investigation of the momentum dependence of vertex functions in gauge theories[2], It is widely accepted that these IR singularities may cause color to be confined and hence produce quark confinement. In particular it is argued [3] that an “effective potential” in momentum space between quarks is proportional to g2(q2)/q2 where g2(q2) is the running coupling constant which is singular in the IR i.e. as q2 → 0. For example if g2(q2)~ l/q2 as q2 → 0 we can crudely translate this into a potential growing linearly with distance for large distances.


Ward Identity Vertex Function Gluon Propagator Tensor Form Dyson Equation 
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  1. 1.
    The work described here was done in collaboration with Phil Lucht, University of Utah, F. Zachariasen, Caltech and M. Baker and co-workers at University of Washington. The preliminary description of this program appears in J. S. Ball and F. Zachariasen, Nucl.Phys. B143, 148 (1978).Google Scholar
  2. 2.
    This work was done in collaboration with T. W. Chiu at University of Utah and publication is awaiting the completion of the complete one loop vértex for QCD..Google Scholar
  3. 3.
    J. M. Cornwall and G. Tiktopoulos, Phys.Rev. D15, 2937 (1977).ADSGoogle Scholar
  4. 4.
    W. Kummer, Acta Phys. Austriaca 41, 315 (1975).MathSciNetGoogle Scholar

Copyright information

© Plenum Press, New York 1980

Authors and Affiliations

  • James S. Ball
    • 1
  1. 1.Physics Dept.University of UtahUSA

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