The unitary representations of the Poincare group in any spacetime dimension

Details The unitary representations of the Poincare group in any spacetime dimension The unitary representations of the Poincare group in any spacetime dimension

2006-11-24

arxiv.org/abs/hep-th/0611263v1

Physics

High Energy Physics

High Energy Physics - Theory

50 pages, no figures, expanded version of the lectures presented at the second Modave summer school in mathematical physics (B

Scientific paper

An extensive group-theoretical treatment of linear relativistic wave 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 wave 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

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