Abstract
The recently proposed infinite-dimensional Lie algebra as a model of a symmetry scheme is studied from the point of view of its representations. We construct the tensor product of two one-particle representations of this algebra and study the reduction problem. A new series of representations having non-linear mass formulas is found. Some physical consequences for two-particle states are also discussed.
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References
Formánek J.: Czech. J. Phys.B 16 (1966), 1.
Havlíček M., Votruba J.: Czech. J. Phys.B 16 (1966), 631.
Haigh F. R., Jordan T. F., Mac Farlane A. J.: Preprint UR-875-1. Department of Physics and Astronomy, University of Rochester, Rochester (New York) 1963.
Pukanski L.: J. Math.10 (1961), 475.
Wigner E. P.: Ann. of Math.40 (1939), 149.
Jordan T. F.: Phys. Rev.140 (1965), B 766.
Stern J.: Czech. J. Phys.B17 (1967), 391.
Formánek J.: Czech. J. Phys.B17 (1967), 99.
von Neumann J.: Ann. of Math.50 (1949), 401.
Formánek J.: Nucl. Phys.87 (1966), 376.
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The authors wish to thank Prof. V. Votruba for constant interest shown throughout this work and J. Formánek for valuable discussions.
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Havlíček, M., Votruba, J. The tensor product of one-particle representations of an infinite-dimensional Lie algebra. Czech J Phys 17, 809–821 (1967). https://doi.org/10.1007/BF01691631
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DOI: https://doi.org/10.1007/BF01691631