Regularization by Dimensional Reduction: Consistency, Quantum Action Principle, and Supersymmetry

It is proven by explicit construction that regularization by dimensional reduction can be formulated in a mathematically consistent way. In this formulation the quantum action principle is shown to hold. This provides an intuitive and elegant relation between the D-dimensional Lagrangian and Ward or Slavnov-Taylor identities, and it can be used in particular to study to what extent dimensional reduction preserves supersymmetry. We give several examples of previously unchecked cases.