No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Matrices of Finite Lorentz Transformations in a Noncompact Basis. I. Discrete Series of O(2, 1)
1.See, for instance, “Session on Infinite Representations of Particles” in Proceedings of the 1967 International Conference on Particles and Fields, University of Rochester, Rochester, N.Y. (Interscience Publishers, New York, 1967).
2.M. Toller, CERN Preprints TH 770 and 780, 1967.
3.H. Bebie and H. Leutwyler, Phys. Rev. Letters 19, 618 (1967);
3.M. Gell‐Mann, D. Horn, and J. Weyers, Proceedings of the International Conference on Particle Physics, Heidelberg, September, 1967.
4.V. Bargmann, Ann. Math. 48, 568 (1947).
4.Other recent papers on this group include: A. O. Barut and C. Fronsdal, Proc. Roy. Soc. (London) A287, 532 (1965);
4.A. Kihlberg, Arkiv Fysik 30, 121 (1965);
4.W. J. Holman III and L. C. Biedenharn, Ann. Phys. 39, 1 (1966);
4.N. Mukunda, J. Math. Phys. 8, 2210 (1967);
4.N. Mukunda, 9, 417 (1968); , J. Math. Phys.
4.J. G. Kuriyan, N. Mukunda, and E. C. G. Sudarshan, J. Math. Phys. 9, 2100 (1968);
4.A. O. Barut and E. C. Phillips, Commun. Math. Phys. 8, 52 (1968).
5.N. Mukunda, Ref. 4. We shall refer to the first of these papers as (A).
6.The more familiar distinction between the discrete and the continuous UIR’s is the statement that in the former the quadratic Casimir invariant is quantized, while in the latter it can assume a continuous set of values.
7.See, for instance, V. Bargmann, Ref. 4.
8.A. O. Barut and E. C. Phillips, Ref. 4.
9.I. M. Gel’fand, M. I. Graev, and N. Ya. Vilenkin, Generalized Functions, (Academic Press Inc., New York and London, 1966), Vol. 5, Chap. VII.
10.Recall that the UIR’s are not needed in the Plancherel formula for whereas the remaining discrete UIR’s are needed.
11.For details, see (A).
12.This may be derived by using, for example, the methods described by J. F. Boyce, R. Delbourgo, A. Salam, and J. Strathdee, “Partial Wave Analysis (Part 1),” ICTP Preprint IC/67/9, Trieste, 1967.
13.Note that both functions and are, by definition, even functions of ν.
14.In Ref. 9, the formulas are appropriate to a discussion of the group We have transcribed them so as to express things in the language of the group These two groups are, of course, isomorphic. Note that the parameter S in Ref. 9 is related to our k via
15.For details concerning the hypergeometric functions, see, for instance, Higher Transcendental Functions, A. Erdélyi, Ed. (McGraw‐Hill Book Co., New York, 1953), Vol. 1, Chap. II;
15.N. N. Lebedev Special Functions and their Applications (Prentice‐Hall, Inc. Englewood Cliffs, N.J., 1965).
16.Both and are, by definition, even functions of μ.
Article metrics loading...
Full text loading...