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Harmonic analysis on the Poincaré group

I. Generalized matrix elements

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Abstract

The generalized matrix elements of the unitary representations of the Poincaré group are computed as eigendistributions of a complete commuting set of infinitestimal operators on the group. The unitary representations of the Poincaré group can be reconstructed from these matrix elements in a Hilbert space of square integrable functions over the space of eigenvalues. Some properties of these distributions (which are measures) are given and some characters are computed from the explicit formulae for the matrix elements.

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References

  1. Lurçat, F.: Quantum field theory and the dynamical role of spin. Physics1, 95 (1964).

    Google Scholar 

  2. Kihlberg, A.: Internal coordinates and explicit representations of the Poincaré group. Nuovo Cimento, Ser. 10,53 A, 592 (1968).

    Google Scholar 

  3. Fuchs, G.: Fields on homogeneous spaces of the Poincaré group. Preprint Ecole Polytechnique, France.

  4. Schweber, S. S.: Introduction to relativistic quantum theory. Evanston-Elmsford: Row and Peterson 1961.

    Google Scholar 

  5. Schwartz, L.: Théorie des Distributions. Tomes I, II. Paris: Hermann 1957/59.

    Google Scholar 

  6. Vilenkin, N. Y.: Special functions and group representations. Moscow: Nauka 1965, (In Russian).

    Google Scholar 

  7. Bargmann, V.: Irreducible unitary representations of the Lorentz group. Ann. Math.48, 568–640 (1947).

    Google Scholar 

  8. Barut, A. O., andC. Frondsdal: On non-compact groups: Representations of the 2+1 Lorentz group. Trieste preprint 1965.

  9. Joos, H., andR. S. Schrader: On the primitive characters of the Poincaré group, Commun. Math. Phys.7, 21–50 (1968).

    Google Scholar 

  10. Fuchs, G., andP. Renouard: The characters of the Poincaré group, Preprint Ecole Polytechnique. France (to appear in J.M.P.).

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Authors and Affiliations

  1. Laboratoire de Physique Théorique et Hautes Energies, Orsay, France

    Nghiem Xuan Hai

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  1. Nghiem Xuan Hai
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In partial fulfilment of the requirements for the degree of Docteur d'Etat ès-Sciences Physiques, Faculté d'Orsay, Université de Paris 1969.

Laboratoire associé au C.N.R.S.

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Hai, N.X. Harmonic analysis on the Poincaré group. Commun.Math. Phys. 12, 331–350 (1969). https://doi.org/10.1007/BF01667318

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  • DOI: https://doi.org/10.1007/BF01667318

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