Two Topics in Quantum Chromodynamics
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?
KeywordsStructure Function Quantum Chromo Dynamic Perturbation Series Absorptive Part Current Correlation Function
Unable to display preview. Download preview PDF.
- 2.R. Field, “Applications of Perturbative QCD,” Addison-Wesley (1989); M. Peskin and D. Schroeder, in preparation.Google Scholar
- 4.More discussion of essentially this point of view can be found in some old lectures of mind; cf. J. Bjorken, Proc. of the SLAC Summer Institute on Particle Physics, Stanford, CA (1979), A. Mosher, ed.; SLAC-REP-224; also preprint SLAC-PUB-2372.Google Scholar
- 6.V. Fadin, V. Khose, and T. Sjostrand, CERN Preprint CERN-TH-5394/89.Google Scholar
- 7.R. P. Feynman, Proc. of the Int. Conf. on High Energy Physics, Aix-en-Provence, vol. 2, E. Cremien-Alcan et al., ed., Saclay, France (1961).Google Scholar
- 9.See, for example, G. Thooft, “The Whys of Subnuclear Physics, Erice 1977,” A. Zichichi, ed., Plenum, New York (1977);Google Scholar
- 10.For a recent review, see S. Maxfield, Proc. of the XXIV Int. Conf. on High Energy Physics, Munich 1988, Springer-Verlag, Berlin, Heidelberg (1989), p. 661.Google Scholar
- 11.An especially complete treatment is given by G. Rossi, U.C. San Diego preprint UCSD-10P10–227.Google Scholar
- 17.Muta’s book, reference 1, contains a thorough exposition.Google Scholar
- 18.More details can be found in Bjorken and Drell, Ref. 4, Chap. 18.Google Scholar
- 19.Analyticity in P 2 has recently been utilized by A. Gorski and B. Ioffe, University of Bern preprint BUTP-89/12.Google Scholar
- 20.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.Google Scholar