The unitary representations of the Poincare group in any spacetime dimension. (arXiv:hep-th/0611263v2 UPDATED)

An extensive group-theoretical treatment of linear relativistic field equations on Minkowski spacetime of arbitrary dimension D>2 is presented in these lecture notes. To start with, the one-to-one correspondence between linear relativistic field equations and unitary representations of the isometry group is reviewed. In turn, the method of induced representations reduces the problem of classifying the representations of the Poincare group ISO(D-1,1) to the classication of the representations of the stability subgroups only. Therefore, an exhaustive treatment of the two most important classes of unitary irreducible representations, corresponding to massive and massless particles (the latter class decomposing in turn into the ``helicity'' and the "infinite-spin" representations) may be performed via the well-known representation theory of the orthogonal groups O(n) (with D-4

Keywords:

• Minkowski space
• Poincaré group
• Covariant transformation
• Isometry group
• Irreducible representation
• Unitary state
• Spacetime
• Pure mathematics
• Representation theory
• Mathematics

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