Noncommutative Grassmannian $U(1)$ sigma model and a Bargmann--Fock
Teoretičeskaâ i matematičeskaâ fizika, Tome 153 (2007) no. 3, pp. 347-357
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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.
@article{TMF_2007_153_3_a1,
author = {A. V. Komlov},
title = {Noncommutative {Grassmannian} $U(1)$ sigma model and a {Bargmann--Fock}},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {347--357},
publisher = {mathdoc},
volume = {153},
number = {3},
year = {2007},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2007_153_3_a1/}
}
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/