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 loop-graphs 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 four-point 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 n-point functions in the tree-graph approximation. Amplitudes that have the singularity structure of Feynman graphs with planar closed loops are constructed which have the infinite Veneziano spin-mass spectrum occupying each internal line. The problem of renormalization is considered and convergent expressions are obtained for proper self-energy part and for the amputated three- and four-point functions. The four-point 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