Artykuł w czasopiśmie
Brak miniatury
Licencja
ClosedAccessDostęp zamknięty
 

Pseudodifferential Weyl Calculus on (Pseudo-)Riemannian Manifolds

Uproszczony widok
dc.abstract.enOne can argue that on flat space Rd, the Weyl quantization is the most natural choice and that it has the best properties (e.g., symplectic covariance, real symbols correspond to Hermitian operators). On a generic manifold, there is no distinguished quantization, and a quantization is typically defined chart-wise. Here we introduce a quantization that, we believe, has the best properties for studying natural operators on pseudo-Riemannian manifolds. It is a generalization of the Weyl quantization—we call it the balanced geodesic Weyl quantization. Among other things, we prove that it maps square-integrable symbols to Hilbert–Schmidt operators, and that even (resp. odd) polynomials are mapped to even (resp. odd) differential operators. We also present a formula for the corresponding star product and give its asymptotic expansion up to the fourth order in Planck’s constant.
dc.affiliationUniwersytet Warszawski
dc.contributor.authorDereziński, Jan
dc.contributor.authorSiemssen, Daniel
dc.contributor.authorLatosiński, Adam
dc.date.accessioned2024-01-25T18:38:20Z
dc.date.available2024-01-25T18:38:20Z
dc.date.issued2020
dc.description.financePublikacja bezkosztowa
dc.description.number5
dc.description.volume21
dc.identifier.doi10.1007/S00023-020-00890-9
dc.identifier.issn1424-0637
dc.identifier.urihttps://repozytorium.uw.edu.pl//handle/item/117524
dc.identifier.weblinkhttp://link.springer.com/content/pdf/10.1007/s00023-020-00890-9.pdf
dc.languageeng
dc.pbn.affiliationphysical sciences
dc.relation.ispartofAnnales Henri Poincare
dc.relation.pages1595-1635
dc.rightsClosedAccess
dc.sciencecloudnosend
dc.titlePseudodifferential Weyl Calculus on (Pseudo-)Riemannian Manifolds
dc.typeJournalArticle
dspace.entity.typePublication