Accession Number : AD0655738

Title :   A HOMOLOGICAL APPROACH TO PARAMETRIC FEYNMAN INTEGRALS,

Corporate Author : CAMBRIDGE UNIV (ENGLAND) DEPT OF APPLIED MATHEMATICS AND THEORETICAL PHYSICS

Personal Author(s) : Boyling,J. B.

Report Date : MAY 1967

Pagination or Media Count : 41

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)

Descriptors :   (*INTEGRALS, QUANTUM THEORY), BOSONS, VECTOR SPACES, PERTURBATION THEORY, MATHEMATICAL ANALYSIS

Subject Categories : Theoretical Mathematics
      Nuclear Physics & Elementary Particle Physics
      Quantum Theory and Relativity

Distribution Statement : APPROVED FOR PUBLIC RELEASE