The connection discovered by M. Sato, T. Miwa and M. Jimbo (SMJ) between the monodromy-preserving deformation theory of the two-dimensional Euclidean Dirac operator and quantum fields is rigorously established for the case of nonreal S¹ monodromy parameters. This connection involves the expression of the associated n-point functions in terms of solutions to deformation equations which arise as necessary conditions for the monodromy exhibited by a class of multivalued solutions of the Euclidean Dirac equation to be preserved under perturbations of branch points. Our approach utilizes recent results involving infinite-dimensional group representations. A lattice version of the n-point function is introduced as a section of a determinant bundle defined over an infinite dimensional Grassmannian. A trivialization for this bundle is singled out so that the corresponding n-point functions behave like Ising correlations in the massive scaling regime. Then the SMJ n-point functions are recovered as the scaled functions. A parallel scaling analysis is carried out with lattice analogues of the Euclidean Dirac wave functions which scale to square-integrable multivalued solutions of the Euclidean Dirac equation and the connection between the SMJ deformation theory and the n-point functions is rigorously established in terms of local Fourier expansion coefficients of these wave functions. These results are presented in detail for two-point functions with the same monodromy associated to each site.
| Identifer | oai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/184357 |
| Date | January 1988 |
| Creators | Davey, Robert Michael. |
| Contributors | Palmer, John, Faschka, Hermann, Pickrell, Ercolani, Nicholas |
| Publisher | The University of Arizona. |
| Source Sets | University of Arizona |
| Language | English |
| Detected Language | English |
| Type | text, Dissertation-Reproduction (electronic) |
| Rights | Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. |
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