We analyze the possibility of description of D-dimensional massless particles by the Lagrangians linear on world-line curvatures k_i, { \cal S}=\sum_{ i=1}^Nc_i\int k_i d{ \tilde s}. We show, that the nontrivial classical solutions of this model are given by space-like curves with zero 2N-th curvature for N\leq[(D-2)/2]. Massless spinning particles correspond to the curves with constant k_{ N+a}/k_{ N-a} ratio. It is shown that only the system with action { \cal S}=c\int k_N d{ \tilde s} leads to irreducible representation of Poincar\'e group. This system has maximally possible number (N+1) of gauge degrees of freedom. Its classical solutions obey the conditions k_{ N+a}=k_{ N-a}, a=1,..., N-1, while first N curvatures k_i remain arbitrary. This solution is specified by coinciding N weights of the massless representation of little Lorentz group, while the remaining weights vanish.
Categories: hep-th