Hamiltonian structure of the nonlinear sigma model in light front coordinates

The classical nonlinear $O(3)$ sigma model is treated in an isotropic coordinate system. The Dirac brackets are calculated for the independent field variables, introduced by stereographic projection, and also for the ordinary field functions, which form a manifestly $O(3)$-invariant system. It is shown that the Dirac brackets satisfy the Jacobi identities only for a nontrivial choice of the boundary conditions.