Publications of the Research Institute for Mathematical Sciences


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Volume 12, Issue 99, 1976, pp. 343–346
DOI: 10.2977/prims/1195196612

Published online: 1976-12-31

Complex-dimensional Integral and Light-cone Singularities

Noboru Nakanishi[1]

(1) Kyoto University, Japan

The notion of a complex-dimensional integral is introduced in the complex n-dimensional Minkowski space. Its basic properties, such as Lorentz invariance, are investigated. Complex-dimensional invariant delta functions Δn(x,m2), Δ(1)n(x,m2), etc. are explicitly calculated in position space. It is proposed to define products of singular functions in the ordinary Minkowski space by analytically continuing the corresponding n-dimensional ones to n=4. The light-cone singularities of [Δ(x,m2)]2, Δ(x,m2) x Δ(1)(x,m2)]2 and Δ(1)(x,m2)]2 are shown to be unambiguously determined in this way.

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Nakanishi Noboru: Complex-dimensional Integral and Light-cone Singularities. Publ. Res. Inst. Math. Sci. 12 (1976), 343-346. doi: 10.2977/prims/1195196612