Lorentz violation, two-time physics, and strings

The aim of this paper is to study the generalization of the relativistic particle recently proposed by Kostelecký. An alternative action for this system is presented, and it is shown that this action can be interpreted as a particle in curved space. Furthermore, the following results are established for the model: (i) there exists a limit where the system has more local symmetries than the usual relativistic particle; (ii) in this limit when Lorentz symmetry is restored, a direct relationship with the two-time physics is determined; (iii) if also Poincaré symmetry is recovered, the action of a relativistic bosonic string is obtained.