New representation for planar Feynman graphs in terms of strings

Journal Article · Mon Jul 01 00:00:00 EDT 1985 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.526901· OSTI ID:5645096

Hong Tuan, R

We study the planar graphs of a massless scalar phi/sup 3/ field theory in d Euclidean dimensions. We show, using a lattice cutoff, that any graph G can be expressed as a function of strings defined on the dual of G (in the sense of graph theory). We furthermore obtain a series expansion of the Feynman graph in powers of (1/d). The powers are proportional to the total length of the strings drawn on d copies of the dual of G for a given subset of these strings which never cross either themselves or each other on the same copy.

• Research Organization: Laboratoire de Physique Theorique et Hautes Energies, Universite de Paris-Sud, Batiment 211, 91405 Orsay Cedex, France
• OSTI ID: 5645096
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 26:7; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANNIHILATION OPERATORS
COMMUTATORS
COMPOSITE MODELS
CONSERVATION LAWS
COUPLING
CREATION OPERATORS
DIAGRAMS
ELECTRODYNAMICS
EQUATIONS
EUCLIDEAN SPACE
EXTENDED PARTICLE MODEL
FEYNMAN DIAGRAM
FIELD THEORIES
GRAPHS
INTEGRAL EQUATIONS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MATRICES
PARTICLE MODELS
POWER SERIES
QUANTUM ELECTRODYNAMICS
QUANTUM FIELD THEORY
QUANTUM OPERATORS
QUARK MODEL
RIEMANN SPACE
SCALAR FIELDS
SERIES EXPANSION
SPACE
STRING MODELS