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

doi:10.1007/s100520100600

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

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.

Publication:

European Physical Journal C

Pub Date:

March 2001

DOI:

10.1007/s100520100600

10.48550/arXiv.quant-ph/0002067

arXiv:

arXiv:quant-ph/0002067

Bibcode:

2001EPJC...19..743K

Keywords:

Feynman Diagram;
Path Integral;
Simple Rule;
Singular Term;
Temporal Integral;
Quantum Physics

E-Print:

Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of paper also at http://www.physik.fu-berlin.de/~kleinert/kleiner_re303/preprint.html

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

Abstract