Open Access
2007 Noncommutative Grassmannian $U(1)$ Sigma-Model and Bargmann-Fock Space
Aleksandr Komlov
J. Geom. Symmetry Phys. 10: 41-50 (2007). DOI: 10.7546/jgsp-10-2007-41-50


We consider the Grassmannian version of the noncommutative $U(1)$ sigma-model, which is given by the energy functional $E(P) = \|[a, P]\|_{HS}^2$, where $P$ is an orthogonal projection on a Hilbert space $H$ and the operator $a: H \to H$ is the standard annihilation operator. Using realization of $H$ as the Bargmann-Fock space, we describe all solutions with one-dimensional image and prove that the operator $[a, P]$ is densely defined on $H$ for some class of projections $P$ with infinite-dimensional image and kernel.


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Aleksandr Komlov. "Noncommutative Grassmannian $U(1)$ Sigma-Model and Bargmann-Fock Space." J. Geom. Symmetry Phys. 10 41 - 50, 2007.


Published: 2007
First available in Project Euclid: 20 May 2017

zbMATH: 1143.81019
MathSciNet: MR2380049
Digital Object Identifier: 10.7546/jgsp-10-2007-41-50

Rights: Copyright © 2007 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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