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

### Submission summary

 Authors (as Contributors): Nicolas Boulanger
Submission information
Date accepted: 2021-06-07
Date submitted: 2021-05-18 11:27
Submitted by: Boulanger, Nicolas
Submitted to: SciPost Physics Lecture Notes
Ontological classification
Specialties:
• 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.

Published as SciPost Phys. Lect. Notes 30 (2021)

### Submission & Refereeing History

Resubmission scipost_202105_00025v1 on 18 May 2021
Submission scipost_202012_00021v1 on 31 December 2020