Integral Representations for Vertex Functions

The third‐order Feynman graph is studied as a function of the three external masses squared for arbitrary real values of the internal masses. Single and double ``dispersion'' relations are derived which, for arbitrary real values of the undispersed variable(s), involve integrations only ov...

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Bibliographic Details
Published in:Journal of mathematical physics 1964-01, Vol.5 (1), p.100-108
Main Authors: Fronsdal, C., Norton, R. E.
Format: Article
Language:English
Subjects:
DIFFERENTIAL EQUATIONS
DISPERSION RELATIONS
ELEMENTARY PARTICLES
FEYNMAN DIAGRAM
FIELD THEORY
INTEGRALS
INTERACTIONS
MASS
MATHEMATICS
NUMERICALS
PHYSICS
SCATTERING
SPECTRA
VERTEX FUNCTIONS
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Summary:The third‐order Feynman graph is studied as a function of the three external masses squared for arbitrary real values of the internal masses. Single and double ``dispersion'' relations are derived which, for arbitrary real values of the undispersed variable(s), involve integrations only over real contours. Tables list the spectral functions for both the single and double integral formulas. In several cases, a non‐Landau singularity (on the forward scattering curve) appears on the ``physical sheet'', but not as a singularity of the physical boundary value.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.1704053