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Theoretical and Mathematical Physics

, Volume 153, Issue 3, pp 1643–1651 | Cite as

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

  • A. V. Komlov
Article

Abstract

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 → 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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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  1. 1.Moscow State UniversityMoscowRussia

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