Feynman diagrams for pedestrians and mathematicians
Abstract
This is a simple mathematical introduction into Feynman diagram technique, which is a standard physical tool to write perturbative expansions of path integrals near a critical point of the action. I start from a rigorous treatment of a finite dimensional case (which actually belongs more to multivariable calculus than to physics), and then use a simple "dictionary" to translate these results to an infinite dimensional case. The standard methods such as gaugefixing and FaddeevPopov ghosts are also included. Resulting Feynman diagram series often may be used rigorously without any references to the initial physical theory (which one may "sweep under the carpet"). This idea is illustrated on an example of the ChernSimons theory, which leads to universal finite type invariants of knots and 3manifolds.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 2004
 DOI:
 10.48550/arXiv.math/0406251
 arXiv:
 arXiv:math/0406251
 Bibcode:
 2004math......6251P
 Keywords:

 Mathematics  Geometric Topology;
 Mathematical Physics;
 Primary: 81T18;
 81Q30;
 Secondary: 57M27;
 57R56
 EPrint:
 Lecture notes for DennisFest. 28 pages, 6 figures