Geodesic
Structure of the canonical uniton factorization of a solution of a noncommutative unitary sigma model
Teoretičeskaâ i matematičeskaâ fizika, Tome 214 (2023) no. 2, pp. 268-275 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is known that each solution $\Phi$ with a nonzero finite energy can be represented up to a multiplicative constant as a composition of finitely many reflections of the special form $\Phi = e^{i\theta}(I-2P_1) \dots (I-2P_n)$. This representation is called the canonical uniton factorization. Orthogonal projections $P_1, \dots, P_n$, called unitons, have finite-dimensional images $\alpha_1, \dots, \alpha_n$. We show that for $1\le j\le n$, the subspaces $\alpha_1+\dots+\alpha_j$ are invariant under the annihilation operator, and the annihilation operator eigenvalues coincide on these subspaces.
Keywords: canonical uniton factorization, noncommutative sigma model. 
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V. V. Bekresheva. Structure of the canonical uniton factorization of a solution of a noncommutative unitary sigma model. Teoretičeskaâ i matematičeskaâ fizika, Tome 214 (2023) no. 2, pp. 268-275. http://geodesic.mathdoc.fr/item/TMF_2023_214_2_a6/

[1] O. Lechtenfeld, A. D. Popov, “Noncommutative multi-solitons in $2+1$ dimensions”, JHEP, 11 (2001), 40, 32 pp., arXiv: hep-th/0106213 | DOI

[2] A. V. Domrin, O. Lechtenfeld, S. Petersen, “Sigma-model solitons in the noncommutative plane: construction and stability analysis”, JHEP, 03 (2005), 045, 34 pp., arXiv: hep-th/0412001 | DOI | MR

[3] A. V. Domrin, “Nekommutativnye unitony”, TMF, 154:2 (2008), 220–239 | DOI | DOI | MR | Zbl

[4] A. V. Domrin, “Prostranstva modulei reshenii nekommutativnoi sigma-modeli”, TMF, 156:3 (2008), 307–327 | DOI | DOI | MR | Zbl

[5] A. V. Domrina, “Petlevye podnyatiya v nekommutativnoi sigma-modeli”, Trudy MIAN, 279 (2012), 72–80 | DOI | MR

[6] A. V. Domrina, “Tselochislennye kharakteristiki reshenii nekommutativnoi sigma-modeli”, TMF, 178:3 (2014), 307–321 | DOI | DOI | MR | Zbl