Geodesic
Noncommutative Grassmannian $U(1)$ sigma model and a Bargmann–Fock
Teoretičeskaâ i matematičeskaâ fizika, Tome 153 (2007) no. 3, pp. 347-357 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a Grassmannian version of the noncommutative $U(1)$ sigma model specified by the energy functional $E(P)=\bigl\|[a,P]\bigr\|_{\mathrm{HS}}^2$, 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. 
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A. V. Komlov. Noncommutative Grassmannian $U(1)$ sigma model and a Bargmann–Fock. Teoretičeskaâ i matematičeskaâ fizika, Tome 153 (2007) no. 3, pp. 347-357. http://geodesic.mathdoc.fr/item/TMF_2007_153_3_a1/

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