Use this URL to cite or link to this record in EThOS: | https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.329248 |
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Title: | The Fermion algebra in quantum statistical mechanics : monodromy fields on Z² and Boson-Fermion correspondence | ||||||
Author: | Watling, Neil Anthony |
ISNI:
0000 0001 3564 0823
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Awarding Body: | University of Warwick | ||||||
Current Institution: | University of Warwick | ||||||
Date of Award: | 1989 | ||||||
Availability of Full Text: |
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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.
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Supervisor: | Not available | Sponsor: | Science and Engineering Research Council | ||||
Qualification Name: | Thesis (Ph.D.) | Qualification Level: | Doctoral | ||||
EThOS ID: | uk.bl.ethos.329248 | DOI: | Not available | ||||
Keywords: | QA Mathematics ; QC Physics | ||||||
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