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On bound states and non-trivial fixed points in quantum field theories Gat, Gil
Abstract
The calculation of the binding energies in Quantum Field Theories (QFT's) is a hard and long standing problem. Even for weakly coupled field theories like QED the extraction of information on bound states from the perturbative expansion is considered an "art". In the first part of this thesis we define those bound states that can be recovered from the perturbative expansion (threshold bound states) and calculate their mass in various models. It is shown that the method of Pade approximation and the Bethe-Salpeter equation (supplemented by a proof of absence of on mass shell singularities) provide a systematic way of calculating threshold bound states masses from the perturbative expansion of the S-matrix. We check these methods on 1+1 and 2+1 dimensional models where there exist a good expansion for the S-Matrix i.e. either weak coupling or 1/N. In the second part of this thesis a less rigorous approach is taken. This part concentrates on the B=2 sector of the SU (3) Skyrme model. We show that one can generate classical configurations (skyrmions) corresponding to bound states of two particles of an effective field theory (the Skyrme model), starting from classical solutions of the euclidean SU(3) Yang-Mills theory. The parity doubling of the ground state in this sector is also investigated. The third and last part deals with non trivial fixed points in QFT's. It is shown that the infra-red fixed point of the chiral phase transition in d=3 is the critical Gross- Neveu model. This is yet another proof to the nonperturbative renormalizability of four- Fermi interactions in 2+1 dimensions. The critical exponents of this phase transition are calculated within the 1/N expansion. The renormalizability of the GN model is also demonstrated explicitly to next to leading order in l/N by calculating β function, effective potential and ultraviolet dimension of various operators. [more abstract]
Item Metadata
Title |
On bound states and non-trivial fixed points in quantum field theories
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1992
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Description |
The calculation of the binding energies in Quantum Field Theories (QFT's) is a hard and
long standing problem. Even for weakly coupled field theories like QED the extraction
of information on bound states from the perturbative expansion is considered an "art".
In the first part of this thesis we define those bound states that can be recovered from
the perturbative expansion (threshold bound states) and calculate their mass in various
models. It is shown that the method of Pade approximation and the Bethe-Salpeter
equation (supplemented by a proof of absence of on mass shell singularities) provide
a systematic way of calculating threshold bound states masses from the perturbative
expansion of the S-matrix. We check these methods on 1+1 and 2+1 dimensional models
where there exist a good expansion for the S-Matrix i.e. either weak coupling or 1/N.
In the second part of this thesis a less rigorous approach is taken. This part concentrates
on the B=2 sector of the SU (3) Skyrme model. We show that one can generate
classical configurations (skyrmions) corresponding to bound states of two particles of
an effective field theory (the Skyrme model), starting from classical solutions of the euclidean
SU(3) Yang-Mills theory. The parity doubling of the ground state in this sector
is also investigated.
The third and last part deals with non trivial fixed points in QFT's. It is shown
that the infra-red fixed point of the chiral phase transition in d=3 is the critical Gross-
Neveu model. This is yet another proof to the nonperturbative renormalizability of four-
Fermi interactions in 2+1 dimensions. The critical exponents of this phase transition
are calculated within the 1/N expansion. The renormalizability of the GN model is
also demonstrated explicitly to next to leading order in l/N by calculating β function, effective potential and ultraviolet dimension of various operators. [more abstract]
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Extent |
5280540 bytes
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Genre | |
Type | |
File Format |
application/pdf
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Language |
eng
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Date Available |
2008-12-19
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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 |
10.14288/1.0085641
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
1992-05
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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.