Abstract
First, a general property of Lie groups is used in the case of the Poincaré group in order to define the one particle phase space. It is eight-dimensional in the general case and six-dimensional for a spinless or massless particle.
Embedding the Poincaré group into the similitude group of space-time permits us to interpret the dilatation operator as a dynamical variable. The connection between the similitude group and field equations is discussed.
Lurçat's ideas on a possible dynamical role of spin and mass-spin spectra of particles (Regge trajectories) are discussed under the point of view of the degrees of freedom.
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This work constitutes a completed version of a preprint entitled “Classical Hamiltonian Formalism for Spin”, Argonne, September, 1966.
On leave from Université de Marseille, France. Work supported in part by the National Science Foundation.
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Bacry, H. Space-time and degrees of freedom of the elementary particle. Commun.Math. Phys. 5, 97–105 (1967). https://doi.org/10.1007/BF01646840
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DOI: https://doi.org/10.1007/BF01646840