l-oscillators from second-order invariant PDEs of the centrally extended conformal Galilei algebras

Autor(es)

Aizawa, N. ^[1] ; Kuznetsova, Z. ^[2] ; Toppan, F. ^[3]

Afiliação do(s) autor(es)

^[1] Osaka Prefecture Univ, Grad Sch Sci, Dept Math & Informat Sci, Sakai, Osaka 5998531 - Japan

^[2] Univ Fed ABC, BR-09210580 Santo Andre, SP - Brazil

^[3] CBPF, BR-22290180 Rio De Janeiro, RJ - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Mathematical Physics; v. 56, n. 3 MAR 2015.
• Citações Web of Science: 9

Resumo

We construct, for any given l = 1/2 + N-0, the second-order, linear partial differential equations (PDEs) which are invariant under the centrally extended conformal Galilei algebra. At the given l, two invariant equations in one time and l + 1/2 space coordinates are obtained. The first equation possesses a continuum spectrum and generalizes the free Schrodinger equation (recovered for l = 1/2) in 1 + 1 dimension. The second equation (the ``l-oscillator{''}) possesses a discrete, positive spectrum. It generalizes the 1 + 1-dimensional harmonic oscillator (recovered for l = 1/2). The spectrum of the l-oscillator, derived from a specific osp(1 vertical bar 2l + 1) h.w.r., is explicitly presented. The two sets of invariant PDEs are determined by imposing (representation-dependent) on-shell invariant conditions both for degree 1 operators (those with continuum spectrum) and for degree 0 operators (those with discrete spectrum). The on-shell condition is better understood by enlarging the conformal Galilei algebras with the addition of certain second-order differential operators. Two compatible structures (the algebra/superalgebra duality) are defined for the enlarged set of operators. (C) 2015 AIP Publishing LLC. (AU)

• Processo FAPESP: 14/03560-0 - Álgebras conformes super-Galileanas de n elevado, suas propriedades e aplicações
• Beneficiário: Zhanna Gennadyevna Kuznetsova
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional