Summary
We show that a significative connection can be established between the three nonconjugate ten-dimensional subalgebras of the conformal algebra and three nonconjugate eleven-dimensional subalgebras of the extended Schrödinger algebra. This connection is performed through the Wigner-Inonü contraction-extension procedure and makes appear, besides the well-known correspondence between the free relativistic particle and the free nonrelativistic one, an interesting relation between the concept of a free relativistic particle in spaces of constant curvature and the concept of a nonrelativistie one in specifical external fields.
Riassunto
Si mostra che si può stabilire un nesso significativo fra le tre sottoalgebre non coniugate decadimensionali dell’algebra conforme e le tre sottoalgebre non coniugate undecadimensionali dell’algebra di Schrödinger estesa. Questo nesso si ottiene con il procedimento di contrazione-estensione di Wigner e Inonü e fa apparire, oltre alla ben nota corrispondenza fra la particella libera relativistica e quella libera non relativistica, una relazione interessante fra il concetto di particella libera relativistica in spazi con curvature costante e il concetto di particella libera non relativistica in specifici campi esterni.
Реэюме
Мы покаэываем, что может быть установлена характерная свяэь между тремя несопряженными десятимерными субалгебрами конформной алгебры и тремя несопряженными одиннадцатимерными субалгебрами расщиренной алгебры Щредингера. Укаэанная свяэь осушествляется череэ процедуру сжатия-растяжения Вигнера-Иноню и устанавливает, помимо хорощо иэвестного соответствия между свободной релятивистской частицей и свободной нерелятивистской частицей, инте-ресную свяэь между концепцией свободной релятивистской частицы в пространствах постоянной кривиэны и концепцией нерелятивистской частицы в некоторых внещних полях.
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Burdet, G., Perrin, M. About the connections between the conformal algebra and the Schrödinger algebra. Nuov Cim A 25, 181–190 (1975). https://doi.org/10.1007/BF02735619
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DOI: https://doi.org/10.1007/BF02735619