Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2001-12-28
Physics
High Energy Physics
High Energy Physics - Theory
28 pages, 2 figures. More comments about the equations of motion have been added
Scientific paper
Using the bicomplex approach we discuss a noncommutative system in two--dimensional Euclidean space. It is described by an equation of motion which reduces to the ordinary sine--Gordon equation when the noncommutation parameter is removed, plus a constraint equation which is nontrivial only in the noncommutative case. We show that the system has an infinite number of conserved currents and we give the general recursive relation for constructing them. For the particular cases of lower spin nontrivial currents we work out the explicit expressions and perform a direct check of their conservation. These currents reduce to the usual sine-Gordon currents in the commutative limit. We find classical ``localized'' solutions to first order in the noncommutativity parameter and describe the Backlund transformations for our system. Finally, we comment on the relation of our noncommutative system to the commutative sine-Gordon system.
Grisaru Marcus T.
Penati Silvia
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