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

### Submission summary

 As Contributors: Nicolas Boulanger Preprint link: scipost_202012_00021v1 Date submitted: 2020-12-31 12:19 Submitted by: Boulanger, Nicolas Submitted to: SciPost Physics Lecture Notes Academic field: Physics Specialties: Representation Theory High-Energy Physics - Theory Mathematical Physics Approach: Theoretical

### Abstract

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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