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The unitary representations of the Poincar\'e group in any spacetime dimension

Xavier Bekaert, Nicolas Boulanger

SciPost Phys. Lect. Notes 30 (2021) · published 14 June 2021


An extensive group-theoretical treatment of linear relativistic field equations on Minkowski spacetime of arbitrary dimension $D\geqslant 3$ is presented. An exhaustive treatment is performed of the two most important classes of unitary irreducible representations of the Poincar\'e group, corresponding to massive and massless fundamental particles. Covariant field equations are given for each unitary irreducible representation of the Poincar\'e group with non-negative mass-squared.

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