  The present work contains a consistent formulation of the methods of
dimensional regularization (DimReg) and minimal subtraction (MS) in Minkowski
position space. The methods are implemented into the framework of perturbative
Algebraic Quantum Field Theory (pAQFT). The developed methods are used to solve
the Epstein-Glaser recursion for the construction of time-ordered products in
all orders of causal perturbation theory. A solution is given in terms of a
forest formula in the sense of Zimmermann. A relation to the alternative
approach to renormalization theory using Hopf algebras is established.
