Accession Number:

AD0718991

Title:

Duality and Feynman Graphs,

Descriptive Note:

Corporate Author:

BELFER GRADUATE SCHOOL OF SCIENCE NEW YORK

Personal Author(s):

Report Date:

1969-07-01

Pagination or Media Count:

91.0

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

Subject Categories:

  • Nuclear Physics and Elementary Particle Physics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE