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 TMF, 2007, Volume 153, Number 3, Pages 347–357 (Mi tmf6140)

Noncommutative Grassmannian $U(1)$ sigma model and a Bargmann–Fock space

A. V. Komlov

M. V. Lomonosov Moscow State University

Abstract: We consider a Grassmannian version of the noncommutative $U(1)$ sigma model specified by the energy functional $E(P)=\|[a,P]\|_{\mathrm{HS}}^2$, where $P$ is an orthogonal projection operator in a Hilbert space $H$ and $a\colon H\to H$ 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.

Keywords: noncommutative $U(1)$ sigma model, Bargmann–Fock space

DOI: https://doi.org/10.4213/tmf6140

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English version:
Theoretical and Mathematical Physics, 2007, 153:3, 1643–1651

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Revised: 09.03.2007

Citation: A. V. Komlov, “Noncommutative Grassmannian $U(1)$ sigma model and a Bargmann–Fock space”, TMF, 153:3 (2007), 347–357; Theoret. and Math. Phys., 153:3 (2007), 1643–1651

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tmf6140
• https://doi.org/10.4213/tmf6140
• http://mi.mathnet.ru/eng/tmf/v153/i3/p347

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This publication is cited in the following articles:
1. A. V. Domrin, “Moduli spaces of solutions of a noncommutative sigma model”, Theoret. and Math. Phys., 156:3 (2008), 1231–1246
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