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An introduction to the fermionic matrix model Marshall, Nicole
Abstract
Matrix models represent statistical theories of discrete random surfaces, and thus to some extent are relevant to the discrete surface interpretations of field theories such as 2D quantum gravity, string theory, lattice gauge theory, and QCD. Hermitian matrix models, in particular, have been extensively studied in connection with continuum field theories. Although these models exhibit inspiring and suggestive features, they are not without limitations, i.-e. the c = 1 barrier and a non-Borel summable free energy expansion. Hence, we introduce an extension to the theory of matrix models, a variation on the theme — the fermionic matrix model. In this work we make a preliminary study of the simplest fermionic matrix models using the insights and experience garnered from the study of the Hermitian matrix model. Our primary resource is the Makeenko-Migdal method of loop equations from which we find that the fermionic 1-matrix model possesses some unique and promising features including a first order multi-critical point and an alternating free energy expansion.. Non-trivial higher dimensional models subject to modified but consistent loop equation techniques prove immune to analysis by these methods alone.
Item Metadata
Title |
An introduction to the fermionic matrix model
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1995
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Description |
Matrix models represent statistical theories of discrete random surfaces, and thus to
some extent are relevant to the discrete surface interpretations of field theories such as
2D quantum gravity, string theory, lattice gauge theory, and QCD. Hermitian matrix
models, in particular, have been extensively studied in connection with continuum field
theories. Although these models exhibit inspiring and suggestive features, they are not
without limitations, i.-e. the c = 1 barrier and a non-Borel summable free energy
expansion. Hence, we introduce an extension to the theory of matrix models, a variation
on the theme — the fermionic matrix model.
In this work we make a preliminary study of the simplest fermionic matrix models
using the insights and experience garnered from the study of the Hermitian matrix
model. Our primary resource is the Makeenko-Migdal method of loop equations from
which we find that the fermionic 1-matrix model possesses some unique and promising
features including a first order multi-critical point and an alternating free energy expansion..
Non-trivial higher dimensional models subject to modified but consistent loop
equation techniques prove immune to analysis by these methods alone.
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Extent |
3508545 bytes
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Genre | |
Type | |
File Format |
application/pdf
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Language |
eng
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Date Available |
2009-01-26
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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 |
10.14288/1.0086951
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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.