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Higher-Spin Symmetries and Deformed Schrödinger Algebra in Conformal Mechanics

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  • Francesco Toppan
  • Mauricio Valenzuela

Abstract

The dynamical symmetries of -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 invariance of the Calogero Conformal Mechanics, an 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.

Suggested Citation

  • Francesco Toppan & Mauricio Valenzuela, 2018. "Higher-Spin Symmetries and Deformed Schrödinger Algebra in Conformal Mechanics," Advances in Mathematical Physics, Hindawi, vol. 2018, pages 1-10, September.
    • Handle: RePEc:hin:jnlamp:6263150
    DOI: 10.1155/2018/6263150
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