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# Accession Number:

## AD0718991

# Title:

## Duality and Feynman Graphs,

# Descriptive Note:

# Corporate Author:

## BELFER GRADUATE SCHOOL OF SCIENCE NEW YORK

# 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

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#