
Accession Number : AD0718991
Title : Duality and Feynman Graphs,
Corporate Author : BELFER GRADUATE SCHOOL OF SCIENCE NEW YORK
Personal Author(s) : Frye,Graham ; Susskind,Leonard
Report Date : 01 JUL 1969
Pagination or Media Count : 91
Abstract : The logical pattern by which channels are filled in relativistic many body processes is examined for Feynman tree and loopgraphs and for the Veneziano formula. The patterns are different in each case, the Veneziano amplitude obeying a quantum logic intermediate between alternative classical set theoretic logics of the two types of Feynman graphs. A vector space of channels is introduced to analyze the fourpoint function. It is emphasized that the duality principle has kinematic, algebraic, and dynamical significance apart from any relation to Regge asymptotic behavior. A procedure is given for modifying Feynman tree graph amplitudes to obtain duality satisfying npoint functions in the treegraph approximation. Amplitudes that have the singularity structure of Feynman graphs with planar closed loops are constructed which have the infinite Veneziano spinmass spectrum occupying each internal line. The problem of renormalization is considered and convergent expressions are obtained for proper selfenergy part and for the amputated three and fourpoint functions. The fourpoint function serves as a model of a dual symmetric scattering amplitude for neutral scalar particles of mass m. (Author)
Descriptors : (*ELEMENTARY PARTICLES, *REGGE POLES), NUCLEAR SPINS, NUCLEAR RESONANCE, NUCLEAR SCATTERING, NUCLEAR ENERGY LEVELS, ASYMPTOTIC SERIES, INTEGRALS, CONVERGENCE, INVARIANCE, DIFFERENTIAL EQUATIONS, QUANTUM THEORY, RELATIVITY THEORY, PERTURBATION THEORY
Subject Categories : Nuclear Physics & Elementary Particle Physics
Distribution Statement : APPROVED FOR PUBLIC RELEASE