Rules for integrals over products of distributions from coordinate independence of path integrals
Abstract
In perturbative calculations of quantummechanical 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 δ 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.
 Publication:

European Physical Journal C
 Pub Date:
 March 2001
 DOI:
 10.1007/s100520100600
 arXiv:
 arXiv:quantph/0002067
 Bibcode:
 2001EPJC...19..743K
 Keywords:

 Quantum Physics
 EPrint:
 Author Information under http://www.physik.fuberlin.de/~kleinert/institution.html . Latest update of paper also at http://www.physik.fuberlin.de/~kleinert/kleiner_re303/preprint.html