  We consider a real massless scalar field in a two-dimensional spacetime,
satisfying Dirichlet or Neumann boundary condition at the instantaneous
position of a moving boundary. For a relativistic law of motion, we show that
Dirichlet and Neumann boundary conditions yield the same radiation force on a
moving mirror when the initial field state is invariant under time
translations. We obtain the exact formulas for the energy density of the field
and the radiation force on the boundary for vacuum, thermal and coherent state.
In the nonrelativistic limit, our results coincide with those found in the
literature.
