Simetrias em teorias de campos relativísticas

Abstract

This work introduces the Lagrangian formulation for relativistic fields and studies some of the consequences of the invariance of these fields under certain types of transformations, namely, spatial translations and Lorentz’s boosts. For this, an abbreviated study of special relativity and how vectors and tensors transform in Minkowski’s space-time is performed. In particular, we study the Noether theorem, which arises as a consequence of the principle of stationary action and which guarantees that for all continuous symmetry in space-time there is a law of conservation. Emphasis is given to the study of the classical electromagnetic field, whose symmetries result in the conservation of the energy and momentum associated with the field, as well as the orbital and spin angular momentum. These quantities are derived from the definitions of energy-momentum tensor and angular momentum associated with the electromagnetic field.