| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [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
Total Affiliations: 3
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| Document type: | Journal article |
| Source: | Journal of Mathematical Physics; v. 56, n. 3 MAR 2015. |
| Web of Science Citations: | 9 |
| Abstract | |
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) | |
| FAPESP's process: | 14/03560-0 - Super-Galilean conformal algebras of higher n, their properties and applications |
| Grantee: | Zhanna Gennadyevna Kuznetsova |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - International |