About: The Shmushkevich Method for Higher Symmetry Groups of Interacting Particles

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Description	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 %22isotopic non-polarization%22 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. 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 %22isotopic non-polarization%22 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. (en)
Title	The Shmushkevich Method for Higher Symmetry Groups of Interacting Particles The Shmushkevich Method for Higher Symmetry Groups of Interacting Particles (en)
skos:prefLabel	The Shmushkevich Method for Higher Symmetry Groups of Interacting Particles The Shmushkevich Method for Higher Symmetry Groups of Interacting Particles (en)
skos:notation	RIV/68407700:21340/13:00210080!RIV14-MSM-21340___
http://linked.open...avai/predkladatel	Fakulta jaderná a fyzikálně inženýrská
http://linked.open...avai/riv/aktivita	Z
http://linked.open...avai/riv/aktivity	Z(MSM6840770039)
http://linked.open...iv/cisloPeriodika	5
http://linked.open...vai/riv/dodaniDat	2014
http://linked.open...aciTvurceVysledku	Chadzitaskos, Goce
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	České vysoké učení technické v Praze / Fakulta jaderná a fyzikálně inženýrská
http://linked.open...dnocenehoVysledku	104958
http://linked.open...ai/riv/idVysledku	RIV/68407700:21340/13:00210080
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	isospin; particle collisions; Lie group representation (en)
http://linked.open.../riv/klicoveSlovo	Lie group representation isospin particle collisions
http://linked.open...odStatuVydavatele	CZ - Česká republika
http://linked.open...ontrolniKodProRIV	[2296307A232F]
http://linked.open...i/riv/nazevZdroje	Acta Polytechnica
http://linked.open...in/vavai/riv/obor	BE
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	4 (xsd:int)
http://linked.open...UplatneniVysledku	2013
http://linked.open...v/svazekPeriodika	53
http://linked.open...iv/tvurceVysledku	Chadzitaskos, Goce Patera, J. Bodner, M. Tereszkiewicz, A.
http://linked.open...n/vavai/riv/zamer	Matematické, počítačové a experimentální metody ve fyzice
issn	1210-2709
number of pages	4 (xsd:int)
http://bibframe.org/vocab/doi	10.14311/AP.2013.53.0395
http://localhost/t...ganizacniJednotka	21340

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