The European Physical Journal C - Particles and Fields

, Volume 19, Issue 4, pp 743–747

Rules for integrals over products of distributions from coordinate independence of path integrals

Authors

  • H. Kleinert
    • Freie Universität Berlin, Institut für Theoretische Physik, Arnimallee 14, 14195 Berlin, Germany
  • A. Chervyakov
    • Freie Universität Berlin, Institut für Theoretische Physik, Arnimallee 14, 14195 Berlin, Germany
Theoretical physics

DOI: 10.1007/s100520100600

Cite this article as:
Kleinert, H. & Chervyakov, A. Eur. Phys. J. C (2001) 19: 743. doi:10.1007/s100520100600

Abstract.

In perturbative calculations of quantum-mechanical path integrals in curvilinear coordinates, one encounters Feynman diagrams involving multiple temporal integrals over products of distributions which are mathematically undefined. In addition, there are terms proportional to powers of Dirac \( \delta \)-functions at the origin coming from the measure of path integration. We derive simple rules for dealing with such singular terms from the natural requirement of coordinate independence of the path integrals.

Copyright information

© Springer-Verlag Berlin Heidelberg 2001