  The particle diffusion in a fluid is a classical topic that dates back to
more than one century ago. However, a full solution to this issue still lacks.
In this work the velocity autocorrelation function and the diffusion constant
are derived analytically, and the hydrodynamics effect on the particle
diffusion is analyzed in detail. Unlike previous studies, the ring-collision
effect is exhaustively considered in our treatment, and the hydrodynamics
approach is extended to the whole time range. Large scale molecular dynamics
simulations for the hard-disk fluid show that our analytical results are valid
up to the density close to the crystallization point.
