Quantum mappings acting by coordinate transformations on Wigner distributions

• Nuno Costa Dias ^[1] ; João Nuno Prata ^[1]
  1. [1] Universidade de Lisboa

     Universidade de Lisboa

     Socorro, Portugal

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 35, Nº 2, 2019, págs. 317-337
• Idioma: inglés
• DOI: 10.4171/rmi/1056
• Texto completo no disponible (Saber más ...)
• Resumen

  • We prove two results about Wigner distributions. Firstly, that the Wigner transform is the only sesquilinear map S(Rn)×S(Rn)→S(R2n) which is bounded and covariant under phase-space translations and linear symplectomorphisms. Consequently, the Wigner distributions form the only set of quasidistributions which is invariant under linear symplectic transformations. Secondly, we prove that the maximal group of (linear or non-linear) coordinate transformations that preserves the set of (pure or mixed) Wigner distributions consists of the translations and the linear symplectic and antisymplectic transformations.