Abstract
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 [Δ(x; m 2)]2, Δ(x; m 2)Δ(1)(x; m 2), and [Δ(1)(x; m 2)]2 are shown to be unambiguously determined in this way.
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Communicated by R. Haag
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Nakanishi, N. Complex-dimensional invariant delta functions and lightcone singularities. Commun.Math. Phys. 48, 97–118 (1976). https://doi.org/10.1007/BF01608498
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DOI: https://doi.org/10.1007/BF01608498