Abstract
Unitary analytic representations of the conformal group are relized on Hilbert spaces of holomoprhic or antiholomorphic functions over a tube domain in complex Minkowski space. The distributional boundary values of these functions are tempered distributions on real Minkowski space. The representations are characterized by an integral scale dimension labeln and two spin labelsj 1 andj 2. The connection between the dimensionn and the degree of singularity of the tempered distribution is investigated. We propose an application to inclusive reactions of elementary particles.
Similar content being viewed by others
References
Graev, M. L.: Dokl. Akad. Nauk SSSR98, 517 (1954).
Esteve, A., Sona, P. G.: Nuovo Cimento32, 473 (1964).
Rühl, W.: The Lorentz Group and Harmonic Analysis, eq. (2–29) New york: W. A. Benjamin, Inc. 1970.
Meschkowski, H.: Hilbertsche Räume mit Kernfunktion. Grundl. Math. Wiss. Bd.113, Berlin-Göttingen-Heidelberg: Springer 1962.
Köthe, G.: Math. Z.57, 13 (1952), J. r. angew. Math.191, 30 (1953).
Tillmann, H. G.: Math. Z.59, 61 (1953),76, 5 (1961),77, 125 (1961).
Neumark, M. A.: Normierte Algebren, p. 224, Berlin: VEB Deutscher Vlg. der Wissenschaften 1959.
Schwartz, L.: Théorie des Distributions, Paris: Hermann 1966.
Streater, R. F., Wightman, A. S.: PCT, Spin and Statistics, and All That, Theorem 2–9, New York: W. A. Benjamin, Inc. 1964.
Ref. 9, Theorem 2–10.
Mack, G., Salam, A.: Ann. Phys.53, 174 (1969).
Mueller, A. H.: Phys. Rev. D2, 2963 (1971).
Frishman, Y.: Ann. Phys.66, 373 (1971) and further literature quoted there.
Müller, V. F., Rühl, W.: University of Trier-Kaiserslautern preprint, November 1971.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Rühl, W. Distributions on Minkowski space and their connection with analytic representations of the conformal group. Commun.Math. Phys. 27, 53–86 (1972). https://doi.org/10.1007/BF01649659
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01649659