Propagator products in arbitrary dimensions

We study the properties of propagator products in<em>x</em>-space in space-time of arbitrary dimension 2<em>l</em>, viewing these products as generalized functions. In this way we investigate such questions as gauge invariance, singularities, communication relations between field operators in perturbation theory, etc. By proceeding carefully to the limit of integer dimensions we are able to show that there are no inconsistencies in the canonical equal-time commutators of fields and that the<em>c</em>-number current-current Schwinger term reduces to ∂_r(∂²)^l-1δ^{2 l-1}(χ) rather than the divergent distribution<em>Λ</em> ^{2 l-2}(∂)_rδ^{2 l-1}(χ). Dimensional regularization is also applied to nonpolynomial interaction Lagrangians: there the close similarity with Mitter's analytic regularization demonstrates that the exponential superpropagator is characterized by a minimal singularity in four dimensions.