  Within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism, we
discuss the full set of proper BRST and anti-BRST transformations for a 2D
diffeomorphism invariant theory which is described by the Lagrangian density of
a standard bosonic string. The above (anti-)BRST transformations are off-shell
nilpotent and absolutely anticommuting. The latter property is valid on a
submanifold of the space of the quantum fields where the 2D version of the
universal (anti-)BRST invariant Curci-Ferrari (CF) type of restrictions are
satisfied. We derive the precise forms of the BRST and anti-BRST invariant
Lagrangian densities as well as the exact expressions for the conserved
(anti-)BRST and ghost charges. The lucid derivation of the proper anti-BRST
symmetry transformations and the emergence of the CF-type restrictions are
completely novel results for our present bosonic string which has already been
discussed earlier in literature where only the BRST symmetry transformations
have been pointed out. We briefly mention the derivation of the CF-type
restrictions from the modified version of Bonora-Tonin superfield approach,
too.
