Citation
Wilson, Kenneth Geddes (1961) An investigation of the Low equation and the ChewMandelstam equations. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd10222002104500
Abstract
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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 onemeson approximation is a double power series in the coupling constant g[superscript 2]and [...]. The method applied by GellMann 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 onemeson approximation for the symmetric scalar pionnucleon interaction; it is a multiplevalued 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 pionpion 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 
Major Option:  Physics 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  1 January 1961 
Record Number:  CaltechETD:etd10222002104500 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd10222002104500 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  4205 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  22 Oct 2002 
Last Modified:  26 Dec 2012 03:06 
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