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Type of Document	Dissertation
Author	Wilson, Kenneth Geddes
URN	etd-10222002-104500
Persistent URL	http://resolver.caltech.edu/CaltechETD:etd-10222002-104500
Title	An investigation of the Low equation and the Chew-Mandelstam equations
Degree	PhD
Option	Physics
Advisory Committee	Advisor Name Title Unknown Committee Member
Keywords	None
Date of Defense	1961-01-01
Availability	unrestricted
Abstract NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. We show that for scalar theories without a cutoff the asymptotic form for large energies [omega] of the perturbation expansion of the Low equation in the one-meson approximation is a double power series in the coupling constant g[superscript 2]and [...]. The method applied by Gell-Mann and Low to the photon propagator in electrodynamics is used to show that if the crossing matrix has only one negative eigenvalue this power series reduces to a series in a single variable [...] where [...], and [...] is a constant. The series in y is evaluated for several interactions and for some crossing matrices with no physical interpretation; for the former the series is a simple algebraic function, while for the latter it usually diverges for all values of y [not equal to] o. We obtain the exact solution of the one-meson approximation for the symmetric scalar pion-nucleon interaction; it is a multiple-valued function of g[superscript 2]. We compare perturbation approximation to the determinantal function of Baker and the cotangent of the phase shift, with the numerical solution of Salzman, for the symmetric pseudoscalar theory with a cutoff; they are found to be often accurate to a few percent. We show that Chew and Mandelstam's approximate equations for pion-pion scattering have no solution for positive coupling [lamda], and that the perturbation expansion of the solution of their equations for isotopic spin o pions diverges for [lamda] [not equal to] o. For pions with I = 1 we present calculations of the perturbation expansion to sixth order in [lamda].
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