Simetrias escondidas na eletrodinˆamica de Podolsky e no magnetismo de Heisenberg

Abstract

In this thesis, it will be revised the main methods of canonical quantization of constrained systems and it will be presented a contemporary technique, the Embedding Symplectic Formalism (ESF), that it embed a second class theory in a dual with gauge invariance. The ESF will be applied to two different systems, namely, Podolsky electrodynamics and two-dimensional isotropic Heisenberg model. It will be analyzed the dual version of the gauge-invariant theory of Maxwell-Proca through the MaxwellPodolsky theory that appears more attractive because it assigns a mass to the photon without violating the symmetries in question. Although they have physical characteristics similar, the spectra are different. The dual description presented here maches the result found in the literature through of the propagator level. It will be discussed two-dimensional isotropic Heisenberg model in terms of constraints system. Such constraints can be used to eliminate some canonical variables from theory. The second class constraints may be used as generators of hidden symmetries. Given a particular choice of factor ordering, will be writing the functional Schrodinger ¨ equation for the original second class Hamiltonian and the first class, which are identical, justifying this choice of factor ordering.