Numerical solutions of lattice quantum fields with a hierarchy of Schroedinger-like equations.

Persistent Link:
http://hdl.handle.net/10150/185265
Title:
Numerical solutions of lattice quantum fields with a hierarchy of Schroedinger-like equations.
Author:
Ludwig, Mark Allen.
Issue Date:
1990
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
Systems of quantized fields can be described by an infinite hierarchy of coupled equations. Such a hierarchy is derived from first principles for a simple interacting field theory to illustrate this type of a representation. The perturbation series for the S matrix is derived from the hierarchy equations in order to show its equivalence to the usual expansion in Feynman amplitudes. An inquiry is then conducted to determine whether this type of representation is useful for solving problems. Truncations of the hierarchy which predict simple bound states are examined in the weak coupling limit, and equations describing a hydrogen-like atom are obtained. Next, the numerical approximation of a truncated hierarchy is studied, and a scattering/particle creation process is modeled in one dimension with a resulting accuracy of 1 to 2 percent. Finally, the mathematical questions of convergence which arise in connection with quantized fields are discussed within the context of the hierarchy equations.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Mathematics; Physics.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Physics; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Morse, R.

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleNumerical solutions of lattice quantum fields with a hierarchy of Schroedinger-like equations.en_US
dc.creatorLudwig, Mark Allen.en_US
dc.contributor.authorLudwig, Mark Allen.en_US
dc.date.issued1990en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractSystems of quantized fields can be described by an infinite hierarchy of coupled equations. Such a hierarchy is derived from first principles for a simple interacting field theory to illustrate this type of a representation. The perturbation series for the S matrix is derived from the hierarchy equations in order to show its equivalence to the usual expansion in Feynman amplitudes. An inquiry is then conducted to determine whether this type of representation is useful for solving problems. Truncations of the hierarchy which predict simple bound states are examined in the weak coupling limit, and equations describing a hydrogen-like atom are obtained. Next, the numerical approximation of a truncated hierarchy is studied, and a scattering/particle creation process is modeled in one dimension with a resulting accuracy of 1 to 2 percent. Finally, the mathematical questions of convergence which arise in connection with quantized fields are discussed within the context of the hierarchy equations.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectMathematicsen_US
dc.subjectPhysics.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplinePhysicsen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorMorse, R.en_US
dc.contributor.committeememberGarcia, J.D.en_US
dc.contributor.committeememberThews, R.en_US
dc.contributor.committeememberParmenter, R.en_US
dc.contributor.committeememberStoner, J.en_US
dc.identifier.proquest9111950en_US
dc.identifier.oclc710365818en_US
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