Abstract
The 2-point functions of Euclidean conformal invariant quantum field theory are looked at as intertwining kernels of the conformal group. In this analysis a fundamental role is played by a two-element groupW, whose non-identity element ℛ=R·I consists of the conformal inversionR multiplied by a space-time reflectionI. The propagators of conformal invariant quantum field theory are determined by the requirement of ℛ-covariance. The importance of the ℛ-inversion in the theory of Zeta-functions is mentioned.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Gel'fand, I.M.: Proc. Int. Congr. Math., Stockholm, p. 74 (1962)
Mack, G.: Renormalization and invariance in quantum field theory. New York: Plenum Press (to appear)
Rühl, W.: Commun. math. Phys.30, 287 (1973);34, 149 (1973)
Ferrara, S., Gatto, R., Grillo, A.: Springer tracts in modern physics, Vol. 67. Berlin-Heidelberg-New York: Springer 1973; Ann. Phys. (N.Y.)76, 161 (1973)
Todorov, I.T.: Conformal invariant quantum field theory with anomalous dimensions, Cargése Lectures (1973)
See for example Warner, G.: Harmonic analysis on semi-simple Lie groups, Vol. I and II. Berlin-Heidelberg-New York: Springer 1972
Ferrara, S., Gatto, R., Grillo, A.F., Parisi, G.: Lett. Nuovo Cimento4, 115 (1972)
Schreier, E.: Phys. Rev. D3, 980 (1971)
Kunze, R.A., Stein, E.M.: Am. J. Math.89, 385 (1967)
Knapp, A.W., Stein, E.M.: Ann. Math.93, 489 (1971)
Kostant, B.: Bull. Am. Math. Soc.75, 627 (1969)
See ref. [6] Vol. I, p. 446
Weyl, H.: The classical groups. Princeton: Univ. Press. 1939
Hirai, T.: Proc. Japan Acad.42, 323 (1965)
Gelfand, I.M., Shilov, G.E.: Generalized functions, Vol. 1, New York: Academic Press 1964
Koller, K.: Homogeneous interactions and a summation method in perturbation theory, Karpacz Lectures (1973)
Gelfand, I.M., Graev, M.I., Vilenkin, N.Y.: Generalized functions, Vol. 5. New York: Academic Press 1966
See for example: Gel'fand, I.M., Graev, M.I., Pyatetskii-Shapiro, I.I.: Representation theory and automorphic functions. W.B. Saunders Co. 1969; Jacquet, H., Langlands, R.P.: Automorphic Forms on GL(2), Lecture Notes in Math., Vol. 114. Berlin-Heidelberg-New York: Springer 1970; Weil, A.: Dirichlet series and automorphic forms. Lecture Notes in Math., Vol. 189, Berlin-Heidelberg-New York: Springer 1971
Author information
Authors and Affiliations
Additional information
Communicated by R. Haag
Rights and permissions
About this article
Cite this article
Koller, K. The significance of conformal inversion in quantum field theory. Commun.Math. Phys. 40, 15–35 (1975). https://doi.org/10.1007/BF01614094
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01614094