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dc.contributor.authorAccardi, Luigi
dc.contributor.authorDhahri, Ameur
dc.date.accessioned2011-10-13T09:41:33Z
dc.date.available2011-10-13T09:41:33Z
dc.date.issued2010
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/7202
dc.language.isoenen
dc.subjectHeisenberg modelen
dc.subjectHilbert spacesen
dc.subjectLie algebrasen
dc.subject.ddc515en
dc.titleThe quadratic Fock functoren
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe construct the quadratic analog of the boson Fock functor. While in the first order (linear) case all contractions on the 1-particle space can be second quantized, the semigroup of contractions that admit a quadratic second quantization is much smaller due to the nonlinearity. The encouraging fact is that it contains, as proper subgroups (i.e., the contractions), all the gauge transformations of second kind and all the a.e. invertible maps of mathd into itself leaving the Lebesgue measure quasi-invariant (in particular, all diffeomorphism of mathd). This allows quadratic two-dimensional quantization of gauge theories, of representations of the Witt group (in fact it continuous analog), of the Zamolodchikov hierarchy, and much more. Within this semigroup we characterize the unitary and the isometric elements and we single out a class of natural contractions.en
dc.relation.isversionofjnlnameJournal of Mathematical Physics
dc.relation.isversionofjnlvol51en
dc.relation.isversionofjnlissue2en
dc.relation.isversionofjnldate2010
dc.relation.isversionofjnlpagesPaper 22113en
dc.relation.isversionofdoihttp://dx.doi.org/10.1063/1.3294771en
dc.identifier.urlsitehttp://arxiv.org/abs/0910.2454en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherAmerican Institute of Physicsen
dc.subject.ddclabelAnalyseen


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