THE SHMUSHKEVICH METHOD FOR HIGHER SYMMETRY GROUPS OF INTERACTING PARTICLES

Authors

  • Mark Bodner MIND Research Institute, 111 Academy Drive, Irvine, CA 92617
  • Goce Chadzitaskos Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Brehová 7, CZ-11519 Praha 1
  • Jiří Patera Centre de Recherches Mathématiques, Université de Montréal, C. P. 6128, succ. Centre-ville, Montréal, H3C 3J7, Québec
  • Agnieszka Tereszkiewitz Institute of Mathematics, University of Bialystok, Akademicka 2, PL-15-267 Bialystok

DOI:

https://doi.org/10.14311/AP.2013.53.0395

Abstract

About 60 years ago, I. Shmushkevich presented a simple ingenious method for computing the relative probabilities of channels involving the same interacting multiplets of particles, without the need to compute the Clebsch-Gordan coefficients. The basic idea of Shmushkevich is “isotopic non-polarization” of the states before the interaction and after it. Hence his underlying Lie group was SU(2). We extend this idea to any simple Lie group. This paper determines the relative probabilities of various channels of scattering and decay processes following from the invariance of the interactions with respect to a compact simple a Lie group. Aiming at the probabilities rather than at the Clebsch-Gordan coefficients makes the task easier, and simultaneous consideration of all possible channels for given multiplets involved in the process, makes the task possible. The probability of states with multiplicities greater than 1 is averaged over. Examples with symmetry groups O(5), F(4), and E(8) are shown.

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Published

2013-10-31

Issue

Vol. 53 No. 5 (2013)

Section

Articles

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How to Cite

Bodner, M., Chadzitaskos, G., Patera, J., & Tereszkiewitz, A. (2013). THE SHMUSHKEVICH METHOD FOR HIGHER SYMMETRY GROUPS OF INTERACTING PARTICLES. Acta Polytechnica, 53(5), 395-398. https://doi.org/10.14311/AP.2013.53.0395