Nonlinear representations of the Poincare group as a possible basis of particle dynamics

Nonlinear representations of the Poincar\'e group are studied as a possible basis for hadron dynamics. In particular we study whether interacting fields are, in general, equally well described by nonlinear representations of the Poincar\'e group as free fields are by linear representations. The fields are identified with group parameters of the appropriate group cosets, thus forming local coordinate systems on the group manifold. On this basis we derive possible interaction Lagrangians, expressed by invariant metrics of the coset spaces. In contrast to the success of nonlinear representations of internal-symmetry groups (chiral groups), we conclude that recently suggested nonlinear representations of the Poincar\'e group are inadequate for describing interacting fields and for deriving particle interactions, mainly because of physically unacceptable features inherent in those representations.