*Article* **Relativistic Symmetries and Hamiltonian Formalism**

#### **Piotr Kosi ´nski \* and Paweł Ma´slanka \***

Faculty of Physics and Applied Informatics, University of Lodz, Narutowicza 68, 90-136 Lodz, Poland **\*** Correspondence: piotr.kosinski@uni.lodz.pl (P.K.); pawel.maslanka@uni.lodz.pl (P.M.)

Received: 30 September 2020; Accepted: 29 October 2020; Published: 1 November 2020

**Abstract:** The relativistic (Poincaré and conformal) symmetries of classical elementary systems are briefly discussed and reviewed. The main framework is provided by the Hamiltonian formalism for dynamical systems exhibiting symmetry described by a given Lie group. The construction of phase space and canonical variables is given using the tools from the coadjoint orbits method. It is indicated how the "exotic" Lorentz transformation properties for particle coordinates can be derived; they are shown to be the natural consequence of the formalism.

**Keywords:** coadjoint orbits; conformal group; Poincaré group
