Wilson, Kenneth Geddes (1961) An investigation of the Low equation and the Chew-Mandelstam equations. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-10222002-104500
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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].
|Item Type:||Thesis (Dissertation (Ph.D.))|
|Degree Grantor:||California Institute of Technology|
|Division:||Physics, Mathematics and Astronomy|
|Thesis Availability:||Public (worldwide access)|
|Defense Date:||1 January 1961|
|Default Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Imported from ETD-db|
|Deposited On:||22 Oct 2002|
|Last Modified:||26 Dec 2012 03:06|
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