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Noncommutative Grassmannian \(U(1)\) sigma model and a Bargmann-Fock space. (English. Russian original) Zbl 1144.81475
Theor. Math. Phys. 153, No. 3, 1643-1651 (2007); translation from Teor. Mat. Fiz. 153, No. 3, 347-357 (2007).
Summary: We consider a Grassmannian version of the noncommutative \(U(1)\) sigma model specified by the energy functional \(E(P) = \| [a, P]\| _{HS} ^{2}\) , where \(P\) is an orthogonal projection operator in a Hilbert space \(H\) and \(a: H \rightarrow H\) is the standard annihilation operator. With \(H\) realized as a Bargmann-Fock space, we describe all solutions with a one-dimensional range and prove that the operator \([a, P]\) is densely defined in \(H\) for a certain class of projection operators \(P\) with infinite-dimensional ranges and kernels.
Editorial remark: The paper is almost identical to the author’s paper [J. Geom. Symmetry Phys. 10, 41–49 (2007; Zbl 1143.81019)].

81R60 Noncommutative geometry in quantum theory
58B34 Noncommutative geometry (à la Connes)
81S05 Commutation relations and statistics as related to quantum mechanics (general)
Full Text: DOI
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