Conformally equivariant quantum Hamiltonians

• C. Duval ^[2] ; V. Ovsienko ^[1]
  1. [1] Centre National de la Recherche Scientifique

     Centre National de la Recherche Scientifique

     París, Francia

     
  2. [2] Université de la Méditerranée and CPT-CNRS, Francia
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 7, Nº. 3, 2001, págs. 291-320
• Idioma: inglés
• DOI: 10.1007/pl00001403
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• Resumen

  • Let (M, g) be a pseudo-Riemannian manifold and Fλ(M) the space of densities of degree λ on M. We study the space D2λ,μ(M) of second-order differential operators from Fλ(M) to Fμ(M) . If (M, g) is conformally flat with signature p - q, then D2λ,μ(M) is viewed as a module over the group of conformal transformations of M. It turns out that, for almost all values of μ−λ , the O(p+1, q+1)-modules D2λ,μ(M) and the space of symbols (i.e., of second-order polynomials on T∗M ) are canonically isomorphic...