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Relativistic few-body quantum mechanics Monahan, Adam Hugh
Abstract
This thesis develops relativistic quantum mechanical models with a finite number of degrees of freedom and the scattering theories associated with these models. Starting from a consideration of the Poincare Group and its irreducible unitary representations, we develop such representations on Hilbert Spaces of physical states of one, two, and three particles. In the two- and three- particle cases, we consider systems in which the particles are non-interacting and in which the particles experience mutual interactions. We are also careful to ensure that for the three-body system, the formalism predicts that subsystems separated by infinite spatial distances behave independently. We next develop the Faddeev equations, which simplify the solution of multi-channel scattering equations. These are specialised to the three-body system introduced earlier and a series solution of the Faddeev Equations is obtained. A simple mechanical model is introduced to provide a heuristic understanding of this solution. The series solution is also expressed in a diagrammatic form complementary to this mechanical model. A system in which particle production and annihilation are allowed is then introduced by working on an Hilbert Space which is the direct sum of the two- and three-body Hilbert Spaces considered earlier. It is found that in this 2-3 system, as the mass operator and the number operators do not commute, it is not possible for a system to simultaneously have a sharply defined mass and number of particles. The Faddeev Equations for this system are then considered, and a series solution of these equations is developed and discussed. It is also shown that the particle production and annihilation potential has a non-trivial effect on pure two-body and three-body scattering. In the last chapter we consider an attempt to derive from a more elementary field theory, using the dressing transformation, a form for the potential coupling the two- and three-body sectors of the Hilbert Space in the 2-3 system. It is found that this method is inherently ambiguous and is not, therefore, able to provide such information.
Item Metadata
Title |
Relativistic few-body quantum mechanics
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1995
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Description |
This thesis develops relativistic quantum mechanical models with a finite number of
degrees of freedom and the scattering theories associated with these models.
Starting from a consideration of the Poincare Group and its irreducible unitary representations,
we develop such representations on Hilbert Spaces of physical states of one,
two, and three particles. In the two- and three- particle cases, we consider systems in
which the particles are non-interacting and in which the particles experience mutual interactions.
We are also careful to ensure that for the three-body system, the formalism
predicts that subsystems separated by infinite spatial distances behave independently.
We next develop the Faddeev equations, which simplify the solution of multi-channel
scattering equations. These are specialised to the three-body system introduced earlier
and a series solution of the Faddeev Equations is obtained. A simple mechanical model
is introduced to provide a heuristic understanding of this solution. The series solution is
also expressed in a diagrammatic form complementary to this mechanical model.
A system in which particle production and annihilation are allowed is then introduced
by working on an Hilbert Space which is the direct sum of the two- and three-body Hilbert
Spaces considered earlier. It is found that in this 2-3 system, as the mass operator and
the number operators do not commute, it is not possible for a system to simultaneously
have a sharply defined mass and number of particles. The Faddeev Equations for this
system are then considered, and a series solution of these equations is developed and
discussed. It is also shown that the particle production and annihilation potential has a
non-trivial effect on pure two-body and three-body scattering.
In the last chapter we consider an attempt to derive from a more elementary field theory, using the dressing transformation, a form for the potential coupling the two- and
three-body sectors of the Hilbert Space in the 2-3 system. It is found that this method
is inherently ambiguous and is not, therefore, able to provide such information.
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Extent |
4401200 bytes
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Genre | |
Type | |
File Format |
application/pdf
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Language |
eng
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Date Available |
2009-01-30
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0099019
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
1995-11
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.