  In this dissertation we develop a theoretical framework in the context of
perturbative QuantumChromoDynamics (pQCD) for studying non-forward scattering
processes. In particular, we investigate a non-forward unequal mass virtual
Compton scattering amplitude by performing the general operator product
expansion (OPE) and the formal renormalization group (RG) analysis.
  We discuss the general tensorial decomposition of the amplitude to obtain the
invariant amplitudes in the non-forward kinematic region. We study the OPE to
identify the relevant operators and their reduced matrix elements, as well as
the corresponding Wilson coefficients. We find that the OPE now should be done
in double moments with new moment variables. There are in the expansion new
sets of leading twist operators which have overall derivatives. They mix under
renormalization in a well-defined way. We compute the evolution kernels from
which the anomalous dimensions for these operators can be extracted. We also
obtain explicitly the lowest order Wilson coefficients.
  In the high energy limit we find the explicit form of the dominantly
contributing anomalous dimensions. We are then able to solve the resulting
renormalization group equations (RGE) and give a prediction of the high energy
behavior of the invariant amplitudes. We find that it is the same as is
indicated by the conventional double leading logarithmic analysis.
