The quadratic Fock functor
Accardi, Luigi; Dhahri, Ameur (2010), The quadratic Fock functor, Journal of Mathematical Physics, 51, 2, p. Paper 22113. http://dx.doi.org/10.1063/1.3294771
TypeArticle accepté pour publication ou publié
External document linkhttp://arxiv.org/abs/0910.2454
Journal nameJournal of Mathematical Physics
American Institute of Physics
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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.
Subjects / KeywordsHeisenberg model; Hilbert spaces; Lie algebras
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Accardi, Luigi; Dhahri, Ameur (2009) Article accepté pour publication ou publié
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Dhahri, Ameur (2009) Article accepté pour publication ou publié