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The quadratic Fock functor

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Date
2010
Link to item file
http://arxiv.org/abs/0910.2454
Dewey
Analyse
Sujet
Heisenberg model; Hilbert spaces; Lie algebras
Journal issue
Journal of Mathematical Physics
Volume
51
Number
2
Publication date
2010
Article pages
Paper 22113
Publisher
American Institute of Physics
DOI
http://dx.doi.org/10.1063/1.3294771
URI
https://basepub.dauphine.fr/handle/123456789/7202
Collections
  • CEREMADE : Publications
Metadata
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Author
Accardi, Luigi
Dhahri, Ameur
Type
Article accepté pour publication ou publié
Abstract (EN)
We 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.

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