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The fermion algebra in quantum statistical mechanics : monodromy fields on Z2 and boson-fermion correspondence
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Watling, Neil Anthony (1989) The fermion algebra in quantum statistical mechanics : monodromy fields on Z2 and boson-fermion correspondence. PhD thesis, University of Warwick.
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WRAP_Theses_Watling_1989.pdf - Submitted Version - Requires a PDF viewer. Download (2577Kb) | Preview |
Official URL: http://webcat.warwick.ac.uk/record=b3229817~S15
Abstract
Monodromy fields on I3 are a family of lattice fields in two dimensions which are a natural generalisation of the two dimensional Ising field occurring in the C*-algebra approach to Statistical Mechanics. A criterion for the critical limit one point correlation of the monodromy field tra(M) at a 6 l3,
Um(#.(M)).
is deduced for matrices M € GL(p, C) having non-negative eigenvalues.
Using this criterion a non-identity 2x2 matrix is found with a finite critical limit one point correlation. The general set of p x p matrices with finite critical limit one point correlations is also considered and a conjecture for the critical limit n point correlations postulated.
The boson-fermion correspondence for the representation of the CAR algebra over L3(Sl, C) defined by the (t,B) KMS state with chemical potential p is considered and the non-bijectivity shown. Using an alternative formulation the correlations are recalculated leading to a determinant identity reminiscent of Saego’s Theorem.
| Item Type: | Thesis (PhD) | ||||
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| Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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| Library of Congress Subject Headings (LCSH): | Fermions, Quantum statistics, Statistical mechanics, Monodromy groups, Interacting boson-fermion models | ||||
| Official Date: | January 1989 | ||||
| Dates: |
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| Institution: | University of Warwick | ||||
| Theses Department: | Mathematics Institute | ||||
| Thesis Type: | PhD | ||||
| Publication Status: | Unpublished | ||||
| Supervisor(s)/Advisor: | Evans, David E. (David Emrys) | ||||
| Sponsors: | Science and Engineering Research Council (Great Britain) | ||||
| Format of File: | |||||
| Extent: | iii, 78, ii leaves : illustrations | ||||
| Language: | eng |
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