Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2004-09-09
Czech.J.Phys. 54 (2004) 1351-1357; Fortsch.Phys. 53 (2005) 500-505
Physics
High Energy Physics
High Energy Physics - Theory
6 pages, 4 figures; talk at the XIIIth International Colloquium Integrable Systems and Quantum Groups in Prague 17-19 June 200
Scientific paper
10.1002/prop.200410210
As I briefly review, 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. I argue that the noncommutative (Moyal) deformation of this procedure should relax the algebraic reduction from U(2)->U(1) to U(2)->U(1)xU(1). The result are novel noncommutative sine-Gordon equations for a pair of scalar fields. The dressing method is outlined for constructing its multi-soliton solutions. Finally, I look at tree-level amplitudes to demonstrate that this model possesses a factorizable and causal S-matrix in spite of its time-space noncommutativity.
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