The unitary representations of the Poincar\'e group in any spacetime dimension
Xavier Bekaert, Nicolas Boulanger
Abstract
An extensive group-theoretical treatment of linear relativistic field equations on Minkowski spacetime of arbitrary dimension D\geqslant 3 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>D</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:math> 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.
Topics & Concepts
Poincaré groupUnitary representationMinkowski spaceIrreducible representationMathematicsCovariant transformationPure mathematicsLorentz groupRepresentation theory of the Lorentz groupUnitary stateGroup (periodic table)SpacetimeRestricted representationInduced representationMathematical physicsFundamental representationPhysicsQuantum mechanicsLie groupLorentz transformationLawPolitical scienceWeightLie algebraNoncommutative and Quantum Gravity TheoriesBlack Holes and Theoretical PhysicsQuantum Electrodynamics and Casimir Effect