Noncommutative Grassmannian U(1) sigma model and a Bargmann-Fock space
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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.
Keywordsnoncommutative U(1) sigma model Bargmann-Fock space
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- 2.J. A. Harvey, “Komaba lectures on noncommutative solitons and D-branes,” arXiv:hep-th/0102076v1 (2001).Google Scholar
- 5.L. Hörmander, The Analysis of Linear Partial Differential Operators: III. Pseudodifferential Operators (Grundlehren Math. Wiss., Vol. 274), Springer, Berlin (1985).Google Scholar
- 8.D. J. Newman and H. S. Shapiro, “Fisher spaces of entire functions,” in: Entire Functions and Related Parts of Analysis (Proc. Sympos. Pure Math., Vol. 11), Amer. Math. Soc., Providence, R. I. (1968), p. 360.Google Scholar
- 9.N. I. Ahiezer, Lectures in the Theory of Approximation [in Russian], Nauka, Moscow (1965).Google Scholar