An introduction to the fermionic matrix model
| Autor: | Marshall, Nicole |
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| Jazyk: | angličtina |
| Rok vydání: | 1995 |
| Druh dokumentu: | Text |
| Popis: | 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. Science, Faculty of Physics and Astronomy, Department of Graduate |
| Databáze: | Networked Digital Library of Theses & Dissertations |
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