C*-Non-Linear Second Quantization |
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Authors: | Luigi Accardi Ameur Dhahri |
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Affiliation: | 1.Volterra Center,University of Roma Tor Vergata,Rome,Italy;2.Department of Mathematics,Chungbuk National University,Seowon-gu, Cheongju,Korea |
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Abstract: | We construct an inductive system of C*-algebras each of which is isomorphic to a finite tensor product of copies of the one-mode n-th degree polynomial extension of the usual Weyl algebra constructed in our previous paper (Accardi and Dhahri in Open Syst Inf Dyn 22(3):1550001, 2015). We prove that the inductive limit C*-algebra is factorizable and has a natural localization given by a family of C*-sub-algebras each of which is localized on a bounded Borel subset of ({mathbb{R}}). Finally, we prove that the corresponding family of Fock states, defined on the inductive family of C*-algebras, is projective if and only if n = 1. This is a weak form of the no-go theorems which emerge in the study of representations of current algebras over Lie algebras. |
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