Introdução aos sistemas vinculados e aos Formalismos Simplético e de Dirac

Abstract

In this dissertation, we have presented two consistent formalisms to treat the dynamics of constrained systems: the Dirac procedure[15], based on an algorithm that replaces the Poisson brackets by a similar structure, and the symplectic method[17], based on the deformation of the symplectic structure of the phase space. We have applied this formalisms to both simple examples and concrete problems from theoretical physics, such as the Proca model and the electromagnetic field. We also studied the symmetries generated by first class constrained systems. We have presented a prove of Dirac's conjecture[3] and showed that a counter-example found in the literature[2] is consistent with the conjecture