SELF-COUPLED REPRESENTATIONS OF THE LORENTZ GROUP AND INFINITE-COMPONENT FERMI FIELDS.

A self-contained exposition is given of the theory of infinitecomponent Majorana fields. The problem of spin and statistics for such fields is specially analysed. More general possibilities for infinite-component Fermi fields (than those transforming under an irreducible self-coupled representation of the Lorentz group) are indicated. The formalism of ladder representations (involving Bose creation and annihilation operators) is used throughout the paper. Most of the results are known (either from old or.-from recent publications) but are presented here in a unified way,their derivation simplified sometimes being / . Among the few new points, we mention 1) the discussion of the quantization of Majorana fields: which specially concerns the Fourier components with space-like momenta; 2) the location of singularities of the matrix elements of some infinite-dimensional representations of SL,(2t C) for complex values of the group parameters and their relation to the failure of the axiomatic proof of TCP and spin and statistics for infinite-component fields.