Abstract
Operator products in quantum field theory on two-dimensional Minkowski space are expanded into a series of local operators by means of the tensor product decomposition theorem for representations of the conformal group. The Thirring model is used as an explicit example. Two types of expansions result. If the operator product acts on the vacuum state, we obtain strictly covariant expansions. In general however, each term in the expansion is only semicovariant.
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Ferrara, S., Gatto, Q., Grillo, A.F.: Nuovo Cimento Lett.2, 1363 (1971); Phys. Rev. D5, 3102 (1972); Phys. Lett.36B, 124 (1971); Ann. Phys. (N.Y.)76, 161 (1973); Springer Tracts in Modern Physics, Vol. 67, p. 1. Berlin, Heidelberg, New York: Springer 1973
Bonora, L., Nuovo Cimento Lett.3, 548 (1972); Bonora, L., Cicciariello, S., Sartori, G., Tonin, M., in: Scale and conformal symmetry in hadron physics. Proc. of the Advanced School of Physics, Frascati, Italy 1972 (R. Gatto ed.). New York: Wiley 1973
Polyakov, A. M.: Non-Hamiltonian approach to the quantum field theory at small distances. Landau Institute for Theoretical Physics Preprint, Chernogolovka, August 1973, and former work quoted there
Swieca, J. A.: Conformal operator expansions in the Minkowski Region. Pontificia Universidade Católica do Rio de Janeiro Preprint, May 1974; B. Schroer, J. A. Swieca, A. H. Völkel, Phys. Rev. D11, 1509 (1975)
Wilson, K.: Phys. Rev.179, 1499 (1969)
Rühl, W., Yunn, B. C.: Representations of the universal covering group ofSU(1, 1) and their bilinear and trilinear invariant forms. Universität Kaiserslautern Preprint, revised version, to appear in J. Math. Phys.
Thirring, W.: Ann. Phys. (N.Y.)3, 91 (1958)
Klaiber, B.: In: Quantum theory and statistical Physics. Lectures in Theoretical Physics, Vol. X-A, p. 141 (A. O. Barut and W. E. Brittin eds.). New York: Gordon and Breach 1968
Dell'Antonio, G. F., Frishman, Y., Zwanziger, D.: Phys. Rev. D6, 988 (1972)
Kupsch, J., Rühl, W., Yunn, B. C.: Ann. Phys. (N.Y.)89, 115 (1975)
Rühl, W.: Acta Phys. Austriaca, Suppl. XIV, 643 (1975)
Schroer, B., Swieca, J. A.: Phys. Rev. D10, 408 (1974)
Slater, L. J.: Generalized hypergeometrie functions. Cambridge: University Press 1966
Rühl, W.: The Lorentz group and harmonic analysis. See the list of references in this book for references to Toller's work. New York: Benjamin 1969
Gradshteyn, I. S., Ryshik, I. M.: Table of Integrals, series and products. New York, London: Academic Press 1965
Ref. [13], p. 34, Eq. (1.8.10)
Rühl, W., Yunn, B. C.: Operator product expansions in conformally covariant quantum field theory, Part II: Semicovariant Expansion. Kaiserslautern: Preprint, November 1975
Mack, G.: In: Renormalization and invariance in quantum field theory, ed. E. R. Caianiello. New York: Plenum Press 1974, pp. 123–157
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Communicated by R. Haag
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Rühl, W., Yunn, B.C. Operator product expansions in conformally covariant quantum field theory. Commun.Math. Phys. 48, 215–233 (1976). https://doi.org/10.1007/BF01617871
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DOI: https://doi.org/10.1007/BF01617871