New integral equation for summing Feynman graph series (phi/sup 3/ ladder graph case)

Journal Article · Sat Aug 01 04:00:00 EDT 1981 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.525126· OSTI ID:6212664

Gilain, C; Levy, D

The Schwinger parameter formalism is used to derive a new integral equation verified by the sum of the ''open amplitudes'' of the ladder graph series with a phi/sup 3/ interaction. We prove the existence of a solution to this equation and of the corresponding Green's function. This solution, for any finite value of the coupling constant, is a finite sum of solutions to Fredholm integral equations plus the sum of a convergent series. Its set of singularities is a set of poles from which the spectrum of Regge poles is obtained.

• Research Organization: CEN-Saclay, Division de la Physique, Boite Postale No. 2, 91190 Gif-sur-Yvette, France
• OSTI ID: 6212664
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 22:8; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AMPLITUDES
COUPLING CONSTANTS
DIAGRAMS
EQUATIONS
FEYNMAN DIAGRAM
FIELD THEORIES
FUNCTIONS
GREEN FUNCTION
INTEGRAL EQUATIONS
INTEGRAL TRANSFORMATIONS
LADDER APPROXIMATION
LAGRANGIAN FIELD THEORY
MELLIN TRANSFORM
PERTURBATION THEORY
QUANTUM FIELD THEORY
REGGE POLES
REGGE TRAJECTORIES
SINGULARITY
TRANSFORMATIONS