Citation
Ruderman, Malvin Avram (1951) I. Electron Decay of the πMeson. II. A NonLinear Field Theory. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/XK5PZD23. https://resolver.caltech.edu/CaltechTHESIS:10022017101440348
Abstract
Part I.
A πmeson decays into µmeson and neutrino at least 1000 times faster than into an electron and a neutrino. After summarizing the difficulties in assuming that electrons or µmesons interact with nucleons through the intermediary of the πmeson, the decay of the π is discussed for the symmetric coupling scheme in which electrons and µmesons interact directly with nucleons. Selection rules rigorously forbid this decay for the most choices of the πmeson field and the form of nuclear βdecay. For the very special case of pseudoscalar meson and pseudovector βdecay (with arbitrary mixtures of scalar, vector and tensor) the decay rate for π → (µ,v) proceeds 10^{4} times as fast as π → (µ,v) and 10^{+3} as fast as π → (photon, e, v). This result is independent of perturbation theory. Agreement with the observed lifetime can be obtained if the divergent integral is cut off at the nucleon Compton wavelength.
Part II.
A unitary theory of particles is investigated, mostly on the classical level. The Dirac and the KleinGordon equations are augmented by simple nonlinear terms. Interpreted as wave equations for classical fields they contain a much richer variety of solutions than the customary linear theories. Particles, instead of having independent existences as singularities, appear only as intense localized regions of strong field. Solutions of the field equations are subject to the boundary condition that the fields be regular everywhere and that all observable integrals be finite. For simple angular and temporal dependence the wave equation reduces to a set of ordinary differential equations. The boundary condition leads to a nonlinear eigenvalue problem whose solutions are systematically described in the phase plane. Numerical solutions are found for some typical cases. The masses of the particles are positive; the number carrying unit charge is small. The scalar field variables can be interpreted in terms of operators according to the usual commutation rules, but the particles are unstable when perturbed by quantum fluctuations. The application of anticommutation rules to the spinor fields has no classical limit. The lack of satisfactory recipe for quantizing classical spinor fields makes the interpretation of the particlelike solutions obscure.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Subject Keywords:  (Physics and Mathematics) 
Degree Grantor:  California Institute of Technology 
Division:  Physics, Mathematics and Astronomy 
Major Option:  Physics 
Minor Option:  Mathematics 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  1 January 1951 
Record Number:  CaltechTHESIS:10022017101440348 
Persistent URL:  https://resolver.caltech.edu/CaltechTHESIS:10022017101440348 
DOI:  10.7907/XK5PZD23 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  10474 
Collection:  CaltechTHESIS 
Deposited By:  Benjamin Perez 
Deposited On:  02 Oct 2017 19:40 
Last Modified:  04 May 2023 17:43 
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