Irreducibility of some unitary representations of the Poincaré group with respect to the Poincaré subsemigroup, I

Author:

Kaneta Hitoshi

Abstract

Since E. Wigner set up a framework of the relativistically covariant quantum mechanics, several aspects of unitary representations of the Poincaré group have been investigated (see [8], [16]). In this paper it will be shown that some unitary representations of the Poincaré group are irreducible, even if they are restricted to the Poincaré semigroup (Theorem 1, 2 and 3).

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference17 articles.

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2. Angelopoulos E. , Decomposition sur le sou-groupe de Poincaré de la represéntation de mass positive et de spin nul du groupe de Poincaré. Ann. Inst. Henri Poincaré XV, no. 4 (1971), 303–320.

3. Tatsuuma N. , Decomposition of Kronecker products of representations of inhomogeneous Lorentz group, Proc. Japan Acad. 38 (1962), 156–160.

4. Radhakrishnan B. and Mukunda N. , Spacelike representations of the inhomogeneous Lorentz group in a Lorentz basis, J. Math. Phys. 15 (1974), 477–490.

5. Lax P. D. and Phillips R. S. , Scattering theory, Academic Press, 1967.

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