  A TQFT in terms of general gauge fixing functions is discussed. In a
covariant gauge it yields the Donaldson-Witten TQFT. The theory is formulated
on a generalized phase space where a simplectic structure is introduced. The
Hamiltonian is expressed as the anticommutator of off-shell nilpotent BRST and
anti-BRST charges. Following original ideas of Witten a time reversal operation
is introduced and an inner product is defined in terms of it. A non-covariant
gauge fixing is presented giving rise to a manifestly time reversal invariant
Lagrangean and a positive definite Hamiltonian, with the inner product
previously introduced. As a consequence, the indefiniteness problem of some of
the kinetic terms of the Witten's action is resolved. The construction allows
then a consistent interpretation of Floer groups in terms of the cohomology of
the BRST charge which is explicitly independent of the background metric.
  The relation between the BRST cohomology and the ground states of the
Hamiltonian is then completely stablished. The topological theories arising
from the covariant, Donaldson-Witten, and non-covariant gauge fixing are shown
to be quantum equivalent by using the operatorial approach.
