  We present a strategy to define non-perturbatively the energy-momentum tensor
in Quantum Chromodynamics (QCD) which satisfies the appropriate Ward identities
and has the right trace anomaly. The tensor is defined by regularizing the
theory on a lattice, and by fixing its renormalization constants
non-perturbatively by suitable Ward identities associated to the Poincare'
invariance of the continuum theory. The latter are derived in thermal QCD with
a non-zero imaginary chemical potential formulated in a moving reference frame.
A renormalization group analysis leads to simple
renormalization-group-invariant definitions of the gluonic and fermionic
contributions to either the singlet or the non-singlet components of the
tensor, and therefore of their form factors among physical states. The lattice
discussion focuses on the Wilson discretization of quark fields but the
strategy is general. Specific to that case, we also carry out the analysis for
the on-shell O(a)-improvement of the energy-momentum tensor. The
renormalization and improvement programs profit from the fact that, as shown
here, the thermal theory enjoys de-facto automatic O(a)-improvement at finite
temperature. The validity of the proposal is scrutinized analytically by a
study to 1-loop order in lattice perturbation theory with shifted and twisted
(for quarks only) boundary conditions. The latter provides also additional
useful insight for a precise non-perturbative calculation of the
renormalization constants. The strategy proposed here is accessible to Monte
Carlo computations, and in this sense it provides a practical way to define
non-perturbatively the energy-momentum tensor in QCD.
