Complex-dimensional invariant delta functions and lightcone singularities

Invariant delta functions (including imaginary-mass case) defined in a complexn-dimensional space-time are explicitly calculated in position space. It is proposed to define products of invariant delta functions in the ordinary Minkowski space by analytically continuing the correspondingn-dimensional ones ton=4. The (not only leading but also non-leading) lightcone singularities of [(x; m²)]², (x; m²)⁽¹⁾(x; m²), and [⁽¹⁾(x; m²)]² are shown to be unambiguously determined in this way.