
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 alphaspace. In the case of singleloop graphs the relevant relative homology groups are computed and the results compared with those obtained by kspace 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 secondtype 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