Title page for ETD etd-042507-084002

Document Type dissertation

Author Name Dick, Frank Albert

Email Address fdick at wpi.edu

URN etd-042507-084002

Title Scalar Field Theories of Nucleon Interactions

Degree PhD

Department Physics

Advisors
John W. Norbury, Advisor
P.K. Aravind, Co-Advisor
Khin Maung Maung, Committee Member

Keywords
ladder approximation
inelastic process
Bethe-Salpeter
BSE
pion
nucleon
scalar field

Date of Presentation/Defense 2007-04-19

Availability unrestricted

Abstract
This dissertation documents the results of two related efforts. Firstly, a model
of nucleon-nucleon (NN) interactions is developed based on scalar field theory.
Secondly, the relativistic 2-body Bethe-Salpeter equation (BSE) is generalized
to handle inelastic processes in the ladder approximation.
Scalar field theory describes the behavior of scalar particles, particles with spin
0. In the present work scalar field theory is used to describe NN interactions
mediated by pion exchange. The scalar theory is applied to nucleons despite
the fact that nucleons are fermions, spin 1/2 particles best described by fourcomponent
Dirac spinor fields. Nevertheless, the scalar theory is shown to give a
good fit to experiment for the total cross sections for several reactions [1]. The
results are consistent with more elaborate spinor models involving one boson
exchange (OBE). The results indicate that the spin and isospin of nucleons can
to some extent be ignored under certain conditions. Being able to ignore spin
and isospin greatly reduces the complexity of the model.
A limitation of the scalar theory is that it does not distinguish between particle
and anti-particle. Consequently one must decide how to interpret the s-channel
diagrams generated by the theory, diagrams which involve particle creation and
annihilation. The issue is resolved by extending the scalar theory to include
electric charge, and formulating NN interactions in terms of complex scalar
fields, which are able to describe both particles and anti-particles.
A generalized Bethe-Salpeter equation (GBSE) is developed to handle inelastic
processes in the ladder approximation. The GBSE, formulated using the scalar
theory, is new, and introduces a systematic method for analyzing families of
coupled reactions. A formalism is developed centered around the amplitude
matrix M' defined for a given Lagrangian. M' gives the amplitudes of a family of reactions that arise from the Lagrangian. The formalism demonstrates how
these amplitudes, to 2nd order, segregate into independent groups of coupled
BSE’s. The GBSE formalism is applied to the coupled BSE (CBSE) of Faassen
and Tjon (FT) [2] for the reaction N+N->N+Delta, showing that the CBSE is
missing a coupling channel, and in the expansion, under counts ladder diagrams.
A proof is given of the equivalence of the series of ladder diagrams generated by
M' and the S-matrix. A section on future work discusses several projects for
further development and application of the GBSE.

Files
dick.pdf

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Document Type	dissertation
Author Name	Dick, Frank Albert
Email Address	fdick at wpi.edu
URN	etd-042507-084002
Title	Scalar Field Theories of Nucleon Interactions
Degree	PhD
Department	Physics
Advisors	John W. Norbury, Advisor P.K. Aravind, Co-Advisor Khin Maung Maung, Committee Member
Keywords	ladder approximation inelastic process Bethe-Salpeter BSE pion nucleon scalar field
Date of Presentation/Defense	2007-04-19
Availability	unrestricted
Abstract This dissertation documents the results of two related efforts. Firstly, a model of nucleon-nucleon (NN) interactions is developed based on scalar field theory. Secondly, the relativistic 2-body Bethe-Salpeter equation (BSE) is generalized to handle inelastic processes in the ladder approximation. Scalar field theory describes the behavior of scalar particles, particles with spin 0. In the present work scalar field theory is used to describe NN interactions mediated by pion exchange. The scalar theory is applied to nucleons despite the fact that nucleons are fermions, spin 1/2 particles best described by fourcomponent Dirac spinor fields. Nevertheless, the scalar theory is shown to give a good fit to experiment for the total cross sections for several reactions [1]. The results are consistent with more elaborate spinor models involving one boson exchange (OBE). The results indicate that the spin and isospin of nucleons can to some extent be ignored under certain conditions. Being able to ignore spin and isospin greatly reduces the complexity of the model. A limitation of the scalar theory is that it does not distinguish between particle and anti-particle. Consequently one must decide how to interpret the s-channel diagrams generated by the theory, diagrams which involve particle creation and annihilation. The issue is resolved by extending the scalar theory to include electric charge, and formulating NN interactions in terms of complex scalar fields, which are able to describe both particles and anti-particles. A generalized Bethe-Salpeter equation (GBSE) is developed to handle inelastic processes in the ladder approximation. The GBSE, formulated using the scalar theory, is new, and introduces a systematic method for analyzing families of coupled reactions. A formalism is developed centered around the amplitude matrix M' defined for a given Lagrangian. M' gives the amplitudes of a family of reactions that arise from the Lagrangian. The formalism demonstrates how these amplitudes, to 2nd order, segregate into independent groups of coupled BSE’s. The GBSE formalism is applied to the coupled BSE (CBSE) of Faassen and Tjon (FT) [2] for the reaction N+N->N+Delta, showing that the CBSE is missing a coupling channel, and in the expansion, under counts ladder diagrams. A proof is given of the equivalence of the series of ladder diagrams generated by M' and the S-matrix. A section on future work discusses several projects for further development and application of the GBSE.
Files	dick.pdf