Quantizing a relativistic free-particle on the light front: some subtle aspects

We use the light-front machinery to study the behavior of a relativistic free particle and obtain the quantum commutation relations from the classical Poisson brackets. We argue that their usual projection onto the light-front coordinates from the covariant commutation relations show that there is an inconsistency in the expected correlation between canonically conjugate variables time x(+) and energy p(-). This incompatibility between canonical conjugate variables in the light front is discussed in the context of Poisson brackets and a suggestion is made on how to avoid it.

Hopf solitons and area-preserving diffeomorphisms of the sphere

We consider a (3+1)-dimensional local field theory defined on the sphere S-2. The model possesses exact soliton solutions with nontrivial Hopf topological charges and an infinite number of local conserved currents. We show that the Poisson bracket algebra of the corresponding charges is isomorphic to that of the area-preserving diffeomorphisms of the sphere S-2. We also show that the conserved currents under consideration are the Noether currents associated to the invariance of the Lagrangian under that infinite group of diffeomorphisms. We indicate possible generalizations of the model.