On the coupling of massless particles to scalar fields

It is investigated if massless particles can couple to scalar fields in a special relativistic theory with classical particles. The only possible obvious theory which is invariant under Lorentz transformations and reparametrization of the affine parameter leads to trivial trajectories (straight lines) for the massless case, and also the investigation of the massless limit of the massive theory shows that there is no influence of the scalar field on the limiting trajectories. On the other hand, in contrast to this result, it is shown that massive particles are influenced by the scalar field in this theory even in the ultra-relativistic limit.Comment: 9 pages, no figures, uses titlepage.sty, LaTeX 2.09 file, submitted to International Journal of Theoretical Physic

Billiard representation for multidimensional multi-scalar cosmological model with exponential potentials

Multidimensional cosmological-type model with n Einstein factor spaces in the theory with l scalar fields and multiple exponential potential is considered. The dynamics of the model near the singularity is reduced to a billiard on the (N-1)-dimensional Lobachevsky space H^{N-1}, N = n+l. It is shown that for n > 1 the oscillating behaviour near the singularity is absent and solutions have an asymptotical Kasner-like behavior. For the case of one scale factor (n =1) billiards with finite volumes (e.g. coinciding with that of the Bianchi-IX model) are described and oscillating behaviour of scalar fields near the singularity is obtained.Comment: 19 pages, Latex, 2 figures; to be published in GR