Limits of Relativistic Systems

Abstract: We investigate the massless and tensionless limit for the relativistic particle and string respectively. The interaction with interesting background fields, such as the electromagnetic field in the particle case and the Kalb-Ramond field in the string case, are also studied. In order to take the massless- and tensionless limit of the corresponding action, a Hamiltonian field theory is used. The invariances under the Poincar ́e group and diffeomorphisms are of great use, and the Weyl invariance in the string case is found particularly useful, since the background metric can be chosen to be flat without loss of generality. We find it useful to study these systems in the transversal gauge, which is the tensionless correspondence to the conformal gauge, in which the action attains a convenient form. Furthermore, we discuss the physical meaning of some of the results, identify some possible further investigations and also some applications in other fields of physics.