XXXVII Workshop on Geometric Methods in Physics 1-7.07.2018 VII School on Geometry and Physics 25-29.06.2018
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# Alexey Isaev

## Two-spinor description of massive particles and relativistic spin projection operators

On the basis of the Wigner unitary representations of the covering group $ISL(2,\mathbb{C})$ of the Poincaré group, we obtain spin-tensor wave functions of free massive particles with arbitrary spin. The wave functions automatically satisfy the Dirac-Pauli-Fierz equations. In the framework of the two-spinor formalism we construct spin-vectors of polarizations and obtain conditions, that fix the corresponding relativistic spin projection operators (Behrends-Fronsdal projection operators). With the help of these conditions we find explicit expressions for relativistic spin projection operators for integer spins (Behrends-Fronsdal projection operators) and then find relativistic spin projection operators for half integer spins. These %relativistic spin projection operators determine the nominators in the propagators of fields of relativistic particles. We deduce generalizations of Behrends-Fronsdal projection operators for arbitrary space-time dimensions $D>2$.

 Event sponsored by: University of Bialystok

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