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.
Highlights
We present here a brief review of some results obtained by our colleagues in collaboration withYves Brihaye and us
Some physicists warn that beauty can lead one astray [3], we are, generally speaking, attached to the idea that adopting symmetry as a guiding principle often leads to the theories with considerable predictive power
One starts with some classical dynamical system defined within the Hamiltonian formalism and applies the canonical quantization procedure consisting in replacing the Poisson brackets by commutators
Summary
We present here a brief review of some results obtained by our colleagues in collaboration with. They concern the old topic of the basic role of space-time symmetries in physics. It appears that some of the main results, which were for the first time obtained and developed in quantum theory, can be described quite precisely on the classical level in the framework of Hamiltonian formalism. Their quantum counterparts are recovered by applying a straightforward canonical quantization procedure. This work is to a great extent based on semiclassical approximation and the description of various symmetries within this approximation. It was always a great pleasure to work with him
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