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Particles and Fields

Eur. Phys. J. C 19, 743-747
DOI: 10.1007/s100520100600

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

H. Kleinert and A. Chervyakov

Freie Universität Berlin, Institut für Theoretische Physik, Arnimallee 14, 14195 Berlin, Germany

(Received: 12 December 2000 / Revised version: 16 January 2001 / Published online: 6 April 2001 -© Springer-Verlag 2001)

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.

© Società Italiana di Fisica, Springer-Verlag 2001