Communications in Mathematical Physics

, Volume 48, Issue 2, pp 97–118 | Cite as

Complex-dimensional invariant delta functions and lightcone singularities

  • Noboru Nakanishi


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; m2)]2, Δ(x; m2(1)(x; m2), and [Δ(1)(x; m2)]2 are shown to be unambiguously determined in this way.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Delta Function 
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Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • Noboru Nakanishi
    • 1
  1. 1.Research Institute for Mathematical SciencesKyoto UniversityKyotoJapan

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