Abstract
Quantum chromodynamics (QCD) has reached a level of credibility and maturity which deserves textbook status. Indeed, textbooks exist1 and others are on the way.2 Nevertheless, to my mind a textbook treatment of QCD is made much more difficult than that of quantum electrodynamics (QED) because of the confinement problem. Even perturbative QCD—which is all that will really be discussed here—suffers this problem. There is no S-matrix theory of quarks and gluons as there is for QED, as given in the LSZ formalism.3 The concept of “on-mass-shell” or “asymptotic” quark and/or gluon is highly suspect. And the typical “Feynman diagram” used in perturbative QCD contains internal quark and gluon lines and external hadron lines. What does that really mean? How does one derive and justify Feynman-rules for such amplitudes in the absence of good control over the confinement question?
Work supported by Department of Energy contract DE-AC03-76SF00515.
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References
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As might be anticipated, I have in mind the line of argument presented in J. Bjorken and S. Drell, “Relativistic Quantum Fields,” McGraw-Hill, New York (1965), chs. 16–17.
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Muta’s book, reference 1, contains a thorough exposition.
More details can be found in Bjorken and Drell, Ref. 4, Chap. 18.
Analyticity in P 2 has recently been utilized by A. Gorski and B. Ioffe, University of Bern preprint BUTP-89/12.
At least to me. This follows either from inspection or from the realization that ρ satisfies the usual renormalization group equation without an inhomogeneous term.
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© 1990 Plenum Press, New York
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Bjorken, J.D. (1990). Two Topics in Quantum Chromodynamics. In: Lévy, M., Basdevant, JL., Jacob, M., Speiser, D., Weyers, J., Gastmans, R. (eds) Particle Physics. NATO ASI Series, vol 223. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-5790-2_7
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DOI: https://doi.org/10.1007/978-1-4684-5790-2_7
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