Remarks on the Convergencc Problem of the Generalized Partial Wave Expansion

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概要

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• The generalized partial wave expansion in terms of irreducible representations of the inhomogeneous Lorentz group is investigated in the O(3, 1) (t=0) case. If we are concerned only with transformations of energy-momentum, the scattering amplitude is shown to be a function on K＼H/K, where H is the little group determined by t and K is the maximal compact group of H. We suggest that the scattering amplitude which does not belong to L^2(H) has an irreducible component of the supplementary series, and show an example. A Hilbert space H^σ larger than L^2 is introduced and Plancherel's formula on H^σ is explicitly shown. The Hilbert space H^σ has the elements corresponding to the supplementary series as well as those of the principal series.

• 理論物理学刊行会の論文
• 1969-01-25

著者

• MURAI Nobuyuki

  Department of Physics, University of Tokyo

• Murai Nobuyuki

  Department Of Physics University Of Tokyo

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