Higher-Spin Symmetries and Deformed Schrödinger Algebra in Conformal Mechanics

Francesco Toppan*, Mauricio Valenzuela

*Autor correspondiente de este trabajo

Producción científica: Contribución a una revistaArtículorevisión exhaustiva

2 Citas (Scopus)

Resumen

The dynamical symmetries of 1+1-dimensional Matrix Partial Differential Equations with a Calogero potential (with/without the presence of an extra oscillatorial de Alfaro-Fubini-Furlan, DFF, term) are investigated. The first-order invariant differential operators induce several invariant algebras and superalgebras. Besides the sl(2)⊕u(1) invariance of the Calogero Conformal Mechanics, an osp2|2 invariant superalgebra, realized by first-order and second-order differential operators, is obtained. The invariant algebras with an infinite tower of generators are given by the universal enveloping algebra of the deformed Heisenberg algebra, which is shown to be equivalent to a deformed version of the Schrödinger algebra. This vector space also gives rise to a higher-spin (gravity) superalgebra. We furthermore prove that the pure and DFF Matrix Calogero PDEs possess isomorphic dynamical symmetries, being related by a similarity transformation and a redefinition of the time variable.

Idioma originalInglés
Número de artículo6263150
PublicaciónAdvances in Mathematical Physics
Volumen2018
DOI
EstadoPublicada - 2018

Nota bibliográfica

Publisher Copyright:
© 2018 Francesco Toppan and Mauricio Valenzuela.

Áreas temáticas de ASJC Scopus

  • Física y Astronomía General
  • Matemáticas aplicadas

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