  The theory of the dynamics of polymers in solution is developed coming from
the hydrodynamic theory of the Brownian motion (BM) and the Rouse-Zimm (RZ)
model. It is shown that the time correlation functions describing the polymer
motion essentially differ from those in the previous RZ models based on the
Einstein theory of BM. The MSD of the polymer coil is at short times
proportional to t^2 (instead of t). At long times it contains additional (to
the Einstein term) contributions, the leading of which is ~ t^{1/2}. The
relaxation of the internal normal modes of the polymer differs from the
traditional exponential decay. This is displayed in the tails of their
correlation functions, the longest-lived being ~ t^{-3/2} in the Rouse limit
and t^{-5/2} in the Zimm case when the hydrodynamic interaction is strong. It
is discussed that the found peculiarities, in particular a slower diffusion of
the coil, should be observable in dynamic scattering experiments. The dynamic
structure factor and the first cumulant of the polymer coil are calculated. The
theory is extended to the situation when the dynamics of the studied polymer is
influenced by the presence of other polymers in dilute solution.
