2009
DOI: 10.1088/1751-8113/42/17/172001
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On analytic descriptions of two-dimensional surfaces associated with the {\bb C} P^{N-1} sigma model

Abstract: We study analytic descriptions of conformal immersions of the Riemann sphere S 2 into the CP N−1 sigma model. In particular, an explicit expression for two-dimensional (2-D) surfaces, obtained from the generalized Weierstrass formula, is given. It is also demonstrated that these surfaces coincide with the ones obtained from the Sym-Tafel formula. These two approaches correspond to parametrizations of one and the same surface in R N 2 −1 .

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Cited by 26 publications
(61 citation statements)
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“…The proof follows immediately from (10). It follows from Property 13 (see formula (21) below) that such products vanish when the derivatives in (14) are identical (both ∂P or both∂P ).…”
Section: Property 10mentioning
confidence: 90%
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“…The proof follows immediately from (10). It follows from Property 13 (see formula (21) below) that such products vanish when the derivatives in (14) are identical (both ∂P or both∂P ).…”
Section: Property 10mentioning
confidence: 90%
“…We use equalities (7) and (9) to replace some of the factors in the numerator with the appropriate traces and then use relation (14) to factor those traces. The invariance of traces under cyclic permutations of factors (after the common factor is canceled) allows obtaininḡ ∂P +1 · P +1 = tr(∂∂P · P ) + tr(∂P ·∂P · P ) P ·∂P tr(∂P · P ·∂P ) .…”
Section: Statementmentioning
confidence: 99%
“…Интегрирование мож-но провести явно для поверхностей, соответствующих проекторам P k , полученным рекуррентно из голоморфного решения. Это дает [14] …”
Section: проекторы и солитонные поверхностиunclassified
“…Докажем равенство (27) другим способом по сравнению с работой [14]. Поверх-ности X k определяются с помощью (26) с точностью до постоянной матрицы (диа-гональные элементы которой однозначно определяются условием, что следы X k об-ращаются в ноль).…”
Section: проекторы и солитонные поверхностиunclassified
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