Abstract:
Poincaré-covariant countable systems of first-order differential equations that describe the states of a particle with fixed mass and arbitrary fixed spin and correspond to positive energy alone are obtained. The conditions of compatibility for these systems are investigated, and a group-theoretical analysis of them is made. The problem of compatibility of manifestly covariant systems of equations is solved for particles of arbitrary spin in the case when the matrix coefficients realize an arbitrary finite-dimensional representation of the algebra $AO(2,3)$. Manifestly covariant finite-dimensional equations for arbitrary spin $s$ that possess nontrivial solutions are proposed.
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