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Spectral properties of the equation (' + ieA) ' u = '?

Elton, Daniel M. (2001) Spectral properties of the equation (' + ieA) ' u = '? Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 131 (5). pp. 1065-1089.

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    Abstract

    We develop a spectral theory for the equation ( + ieA) × u = ±mu on Minkowski 3-space (one time variable and two space variables); here, A is a real vector potential and the vector product is defined with respect to the Minkowski metric. This equation was formulated by Elton and Vassiliev, who conjectured that it should have properties similar to those of the two-dimensional Dirac equation. Our equation contains a large parameter c (speed of light), and this motivates the study of the asymptotic behaviour of its spectrum as c → +∞. We show that the essential spectrum of our equation is the same as that of Dirac (theorem 3.1), whereas the discrete spectrum agrees with Dirac to a relative accuracy δλ/mc2 ~ O(c−4) (theorem 3.3). In other words, we show that our equation has the same accuracy as the two-dimensional Pauli equation, its advantage over Pauli being relativistic invariance.

    Item Type: Article
    Journal or Publication Title: Proceedings of the Royal Society of Edinburgh: Section A Mathematics
    Additional Information: The final, definitive version of this article has been published in the Journal, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 131 (5), pp 1065-1089 2001, © 2001 Cambridge University Press. RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics
    Subjects: Q Science > QA Mathematics
    Departments: Faculty of Science and Technology > Mathematics and Statistics
    ID Code: 2394
    Deposited By: ep_importer
    Deposited On: 01 Apr 2008 09:18
    Refereed?: Yes
    Published?: Published
    Last Modified: 09 Oct 2013 13:12
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/2394

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