Abstract
For massless models of quantum field theory, some general theorems are proved concerning the analytic continuation of the renormalization group functions as well as the effective coupling and the propagators. Starting points are analytic properties of the effective coupling and the propagators in the momentum variablek 2, which can be converted into analyticity of β- and γ-functions in the coupling parameter λ. It is shown that the β-function can have branch point singularities related to stationary points of the effective coupling as a function ofk 2. The type of these singularities of β(λ) can be determined explicitly. Examples of possible physical interest are extremal values of the effective coupling at space-like points in the momentum variable, as well as complex conjugate stationary points close to the realk 2-axis. The latter may be related to the sudden transition between weak and strong coupling regimes in quantum chromodynamics. Finally, for the effective coupling and for the propagators, the analytic continuation in both variablesk 2 and λ is discussed.
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References
Eckmann, J.-P., Magnen, J., Sénéor, R.: Commun. Math. Phys.39, 251–271 (1975)
Glimm, J., Jaffe, A., Spencer, T.: The cluster expansion in constructive quantum field theory. In: Lecture Notes in Physics, Vol. 25. Berlin, Heidelberg, New York: Springer 1973
Khuri, N.N.: Phys. Rev. D12, 2298–2310 (1975)
t' Hooft, G.: Can we make sense out of quantum Chromodynamics? In: The whys of subnuclear physics (Erice 1977), pp. 943–971. New York: Plenum Press 1979
Oehme, R.: Phys. Lett.71B, 169–171 (1977)
Oehme, R., Zimmermann, W.: Phys. Lett.79B, 314–316 (1978)
Oehme, R., Zimmermann, W.: Phys. Lett.100B, 273–275 (1981)
Gross, D.: 1975 Les Houches Lectures. In: Methods in Field Theory, pp. 162–191. Amsterdam: North-Holland 1976
Ovrut, B., Schnitzer, H.: Low energy and threshold calculations using effective field theory. Nucl. Phys. B (to be published)
Oehme, R., Zimmermann, W.: Phys. Lett.79B, 93–96 (1978)
Popović, D.: Prog. Theor. Phys.58, 300–315 (1977)
Callan, C., Gross, D.: Private communication
Kogut, J.: Progress in lattice gauge theory, Santa Barbara Report NSF-ITP-80-16
Gross, D.: A review of the semiclassical approach to QCD, Princeton Report, 1980
Khuri, N.: Phys. Rev. D23, 2285 (1981)
Epstein, H., Iliopoulos, J.: The arbitrariness in the perturbation series in non-abelian gauge theories (preprint) Laboratoire de Physique Theórique de l'Ecole Normale Superieure, 1981
Khuri, N., McBryan, O.: Phys. Rev. D20, 881–886 (1979)
Adler, S.: Phys. Rev. D23, 2905 (1981)
Frishman, Y., Horsley, R., Wolff, U.: Phys. Lett.96B, 302 (1980)
Curci, G., Ferrari, R.: Nuovo Cimento35A, 273–279 (1976); Phys. Lett.63B, 91–93 (1976)
Kugo, T., Ojima, I.: Phys. Lett.73B, 459–461 (1978); Prog. Theor. Phys.60, 1869–1889 (1978);61, 294–314 (1979); Prog. Theor. Phys. Suppl. No.66 (1979)
Oehme, R., Zimmermann, W.: Phys. Rev. D21, 1661–1671 (1980)
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Communicated by R. Stora
On leave from the Max-Planck-Institut für Physik und Astrophysik, D-8000 München, Federal Republic of Germany
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Oehme, R., Zimmermann, W. Analyticity of effective coupling and propagators in massless models of quantum field theory. Commun.Math. Phys. 85, 363–379 (1982). https://doi.org/10.1007/BF01208720
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DOI: https://doi.org/10.1007/BF01208720