A Gaussian approximation to the effective potential
This thesis investigates some of the properties of a variational approximation to scalar field theories: a trial wavefunctional which has a gaussian form is used as a ground state ansatz for an interacting scalar field theory - the expectation value of the Hamiltonian in this state is then minimized...
Main Author: | |
---|---|
Language: | English |
Published: |
University of British Columbia
2010
|
Subjects: | |
Online Access: | http://hdl.handle.net/2429/26500 |
id |
ndltd-UBC-oai-circle.library.ubc.ca-2429-26500 |
---|---|
record_format |
oai_dc |
spelling |
ndltd-UBC-oai-circle.library.ubc.ca-2429-265002018-01-05T17:43:41Z A Gaussian approximation to the effective potential Morgan, David C. Scalar field theory Physics -- Approximation methods Gaussian processes This thesis investigates some of the properties of a variational approximation to scalar field theories: a trial wavefunctional which has a gaussian form is used as a ground state ansatz for an interacting scalar field theory - the expectation value of the Hamiltonian in this state is then minimized. This we call the Gaussian Approximation; the resulting effective potential we follow others by calling the Gaussian Effective Potential (GEP). An equivalent but more general finite temperature formalism is then reviewed and used for the calculations of the GEP in this thesis. Two scalar field theories are described: ϕ⁴ theory in four dimensions (ϕ⁴₄) and ϕ⁶ theory in three dimensions (ϕ⁶₃). After showing what the Gaussian Approximation does in terms of Feynman diagrams, renormalized GEP's are calculated for both theories. Dimensional Regularization is used in the renormalization and this this is especially convenient for the GEP in ϕ⁶₃ theory because it becomes trivially renor-malizable. It is noted that ϕ⁶₃ loses its infrared asymptotic freedom in the Gaussian Approximation. Finally, it is shown how a finite temperature GEP can be calculated by finding low and high temperature expansions of the temperature terms in ϕ⁶₃ theory. Science, Faculty of Physics and Astronomy, Department of Graduate 2010-07-16T00:38:41Z 2010-07-16T00:38:41Z 1987 Text Thesis/Dissertation http://hdl.handle.net/2429/26500 eng 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. University of British Columbia |
collection |
NDLTD |
language |
English |
sources |
NDLTD |
topic |
Scalar field theory Physics -- Approximation methods Gaussian processes |
spellingShingle |
Scalar field theory Physics -- Approximation methods Gaussian processes Morgan, David C. A Gaussian approximation to the effective potential |
description |
This thesis investigates some of the properties of a variational approximation to scalar field theories: a trial wavefunctional which has a gaussian form is used as a ground state ansatz for an interacting scalar field theory - the expectation value of the Hamiltonian in this state is then minimized. This we call the Gaussian Approximation; the resulting effective potential we follow others by calling the Gaussian Effective Potential (GEP). An equivalent but more general finite temperature formalism is then reviewed and used for the calculations of the GEP in this thesis. Two scalar field theories are described: ϕ⁴ theory in four dimensions (ϕ⁴₄) and ϕ⁶ theory in three dimensions (ϕ⁶₃). After showing what the Gaussian Approximation does in terms of Feynman diagrams, renormalized GEP's are calculated for both theories. Dimensional Regularization is used in the renormalization and this this is especially convenient for the GEP in ϕ⁶₃ theory because it becomes trivially renor-malizable. It is noted that ϕ⁶₃ loses its infrared asymptotic freedom in the Gaussian Approximation. Finally, it is shown how a finite temperature GEP can be calculated by finding low and high temperature expansions of the temperature terms in ϕ⁶₃ theory. === Science, Faculty of === Physics and Astronomy, Department of === Graduate |
author |
Morgan, David C. |
author_facet |
Morgan, David C. |
author_sort |
Morgan, David C. |
title |
A Gaussian approximation to the effective potential |
title_short |
A Gaussian approximation to the effective potential |
title_full |
A Gaussian approximation to the effective potential |
title_fullStr |
A Gaussian approximation to the effective potential |
title_full_unstemmed |
A Gaussian approximation to the effective potential |
title_sort |
gaussian approximation to the effective potential |
publisher |
University of British Columbia |
publishDate |
2010 |
url |
http://hdl.handle.net/2429/26500 |
work_keys_str_mv |
AT morgandavidc agaussianapproximationtotheeffectivepotential AT morgandavidc gaussianapproximationtotheeffectivepotential |
_version_ |
1718593108080328704 |