Requiring an infinite number of conserved local charges or the existence of an underlying linear system does not uniquely determine the Moyal deformation of (1 + 1)-dimensional integrable field theories. As an example, the sine-Gordon model may be obtained by dimensional and algebraic reduction from (2 + 2)-dimensional self-dual U(2) Yang-Mills through a (2 + 1)-dimensional integrable U(2) sigma model, with some freedom in the noncommutative extension of this algebraic reduction. Relaxing the latter from U(2) --> U(1) to U(2) --> U(1) x U(1), we arrive at novel noncommutative sine-Gordon equations for a pair of scalar fields. The dressing method is employed to construct its multi-soliton solutions. Finally, we evaluate various tree-level amplitudes to demonstrate that our model possesses a factorizable and causal S-matrix in spite of its time-space noncommutativity. (C) 2004 Elsevier B.V. All rights reserved.

Lechtenfeld, O., Mazzanti, L., Penati, S., Popov, A., Tamassia, L. (2005). Integrable noncommutative sine-Gordon model. NUCLEAR PHYSICS. B, 705(3), 477-503 [10.1016/j.nuclphysb.2004.10.050].

Integrable noncommutative sine-Gordon model

PENATI, SILVIA;
2005

Abstract

Requiring an infinite number of conserved local charges or the existence of an underlying linear system does not uniquely determine the Moyal deformation of (1 + 1)-dimensional integrable field theories. As an example, the sine-Gordon model may be obtained by dimensional and algebraic reduction from (2 + 2)-dimensional self-dual U(2) Yang-Mills through a (2 + 1)-dimensional integrable U(2) sigma model, with some freedom in the noncommutative extension of this algebraic reduction. Relaxing the latter from U(2) --> U(1) to U(2) --> U(1) x U(1), we arrive at novel noncommutative sine-Gordon equations for a pair of scalar fields. The dressing method is employed to construct its multi-soliton solutions. Finally, we evaluate various tree-level amplitudes to demonstrate that our model possesses a factorizable and causal S-matrix in spite of its time-space noncommutativity. (C) 2004 Elsevier B.V. All rights reserved.
Articolo in rivista - Articolo scientifico
Two dimensional integrable models, noncommutative theories, noncommutative sine-Gordon model
English
2005
705
3
477
503
none
Lechtenfeld, O., Mazzanti, L., Penati, S., Popov, A., Tamassia, L. (2005). Integrable noncommutative sine-Gordon model. NUCLEAR PHYSICS. B, 705(3), 477-503 [10.1016/j.nuclphysb.2004.10.050].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/3284
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