  Hollands and Wald's technique based on *-algebras of Wick products of field
operators is strightforwardly generalized to define the stress-energy tensor
operator in curved globally hyperbolic spacetimes. In particular, the locality
and covariance requirement is generalized to Wick products of differentiated
quantum fields. The proposed stress-energy tensor operator is conserved and
reduces to the classical form if field operators are replaced by classical
fields satisfying the equation of motion. The definition is based on the
existence of convenient counterterms given by certain local Wick products of
differentiated fields. They are independent from the arbitrary length scale
(and any quantum state) and they classically vanish on solutions of field
equation. The averaged stress-energy tensor with respect to Hadamard quantum
states can be obtained by an improved point-splitting renormalization procedure
which makes use of the nonambiguous part of the Hadamard parametrix only that
is completely determined by the local geometry and the parameters which appear
in the Klein-Gordon operator. The averaged stress-energy tensor also coincides
with that found by employing the local $\zeta$-function approach.
