A HOMOLOGICAL APPROACH TO PARAMETRIC FEYNMAN INTEGRALS,
Abstract
The methods of homology theory are applied to Feynman integrals in alpha-space. In the case of single-loop graphs the relevant relative homology groups are computed and the results compared with those obtained by k-space methods. For graphs with more than one loop the permanent pinch difficulty is overcome by modifying the ambient manifold and applying Thom's isotopy theorem. Pinching conditions are then found for Landau singularities in which complete circuits are contracted out and for mixed second-type singularities. The breakdown of the hierarchical principle in perturbation theory is also explained from this point of view. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1967
- Accession Number
- AD0655738
Entities
People
- J. B. Boyling
Organizations
- University of Cambridge