Noncommutative Chern-Simons soliton

We have studied noncommutative extension of the relativistic Chern-Simons-Higgs model, in the first nontrivial order in θ, with only spatial noncommutativity. Both Lagrangian and Hamiltonian formulations of the problem have been discussed, with the focus being on the canonical and symmetric forms of the energy-momentum tensor. In the Hamiltonian scheme, constraint analysis and the induced Dirac brackets have been provided. The space-time translation generators and their actions on the fields are discussed in detail. The effects of noncommutativity on the soliton solutions have been analyzed thoroughly and we have come up with some interesting observations. Considering the relative strength of the noncommutative effects, we have shown that there is a universal character in the noncommutative correction to the magnetic field--it depends only on θ. On the other hand, in the cases of all other observables of physical interest, such as the potential profile, soliton mass, or the electric field, θ as well as τ (the latter comprised solely of commutative Chern-Simons-Higgs model parameters) appear on similar footings. Lastly, we have shown that noncommutativity imposes a further restriction on the form of the Higgs field so that the Bogomolny-Prasad-Sommerfeld equations are compatible with the full variational equations of motion