Abstract
Any finite-energy solution of a noncommutative sigma model has three nonnegative integer-valued characteristics: the normalized energy e(Φ), canonical rank r(Φ), and minimum uniton number u(Φ). We prove that r(Φ) ≥ u(Φ) and e(Φ) ≥ u(Φ)(u(Φ) + 1)/2. Given any numbers e, r, u ∈ ℕ that satisfy the slightly stronger inequalities r ≥ u and e ≥ r +u(u − 1)/2, we construct a finite-energy solution Φ with e(Φ) = e, r(Φ) = r, and u(Φ) = u.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 178, No. 3, pp. 307–321, March, 2014.
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Domrina, A.V. Integer-valued characteristics of solutions of the noncommutative sigma model. Theor Math Phys 178, 265–277 (2014). https://doi.org/10.1007/s11232-014-0142-5
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DOI: https://doi.org/10.1007/s11232-014-0142-5