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Integrable String Models in Terms of Chiral Invariants of SU(n), SO(n), SP(n) Groups
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2008, том 4
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Integrable String Models in Terms of Chiral Invariants of SU(n), SO(n), SP(n) Groups
Інший ID:
2000 Mathematics Subject Classification: 81T20; 81T30; 81T40; 37J35; 53Z05; 22E70
Посилання:
Integrable String Models in Terms of Chiral Invariants of SU(n), SO(n), SP(n) Groups / V.D. Gershun // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 30 назв. — англ.
Підтримка:
This paper is a contribution to the Proceedings of the Seventh International Conference “Symmetry in Nonlinear Mathematical Physics” (June 24–30, 2007, Kyiv, Ukraine). The author would like to thank J.A. de Azcarraga for the stimulating discussion about nonprimitive invariant tensors on simple Lie algebras.
Дата:
2008
Переглядів:
509
Завантажень:
240
Анотація:
We considered two types of string models: on the Riemmann space of string coordinates with null torsion and on the Riemman-Cartan space of string coordinates with constant torsion. We used the hydrodynamic approach of Dubrovin, Novikov to integrable systems and Dubrovin solutions of WDVV associativity equation to construct new integrable string equations of hydrodynamic type on the torsionless Riemmann space of chiral currents in first case. We used the invariant local chiral currents of principal chiral models for SU(n), SO(n), SP(n) groups to construct new integrable string equations of hydrodynamic type on the Riemmann space of the chiral primitive invariant currents and on the chiral non-primitive Casimir operators as Hamiltonians in second case. We also used Pohlmeyer tensor nonlocal currents to construct new nonlocal string equation.
