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πN Partial Wave Relations from Fixed‐ t Dispersion Relations
Author(s) -
Baacke J.,
Steiner F.
Publication year - 1970
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.19700180104
Subject(s) - dispersion relation , mathematics , amplitude , kernel (algebra) , mathematical analysis , convergence (economics) , partial differential equation , dispersion (optics) , partial derivative , physics , mathematical physics , quantum electrodynamics , pure mathematics , quantum mechanics , economics , economic growth
Starting from fixed‐ t dispersion relations we derive a set of relations for the πN partial wave amplitudes, generalizing previous work of O EHME [ 1 ], C APPS and T AKEDA [ 2 ], and C HEW , G OLDBERGER , L OW and N AMBU [ 3 ]. Our relations contain a single integral kernel, which is agiven in a closed form valid for arbitrary angular momentum. This kernel correlates the imaginary parts of all partial wave amplitudes with the partial wave amplitude under consideration. The partial wave relations give the correct threshold behaviour. The region of convergence is determined in the case of axiomatic field theory and in the case of Mandelstam analyticity. Possible applications are discussed.