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. ChervyakovFreie 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)
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 
-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
