Canonical Formulation of Singular Systems

Abstract

Some physical systems are studied as singular systems. Both the canonical formulation (G¨uler’s method) and Dirac’s method are used throughout this work. The equations of motion described by G¨uler are total differential equations in many variables. They are integrable if and only if the integrability conditions are identically satisfied. The solutions of these equations give the fields, which describe the trajectories of the system. Various applications, namely the relativistic spinless particle system and the spinning particle or super-gravity in one dimension, are investigated by using the above formulations. The relativistic classical spinning particle system with second-order Lagrangian is also studied by using the same methods. A comparison between the two approaches is held. The results are found in exact agreement, that indicates the validity of the study