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Title: The Stationary Maxwell-Dirac Equations
Contributor(s): Radford, Christopher John (author)
Publication Date: 2003
DOI: 10.1088/0305-4470/36/20/321
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Abstract: The Maxwell–Dirac equations are the equations for electronic matter, the 'classical' theory underlying QED. The system combines the Dirac equations with the Maxwell equations sourced by the Dirac current. A stationary Maxwell–Dirac system has ψ = e⁻[iEt],φ with φ independent of t. The system is said to be isolated if the dependent variables obey quite weak regularity and decay conditions. In this paper, we prove the following strong localization result for isolated, stationary Maxwell–Dirac systems,• there are no embedded eigenvalues in the essential spectrum, i.e. −m ≤ E ≤ m;• if |E| < m then the Dirac field decays exponentially as |x| → ∞;• if |E| = m then the system is 'asymptotically' static and decays exponentially if the total charge is non-zero.
Publication Type: Journal Article
Source of Publication: Journal of Physics A: Mathematical and General, 36(20), p. 5663-5681
Publisher: Institute of Physics Publishing
Place of Publication: United Kingdom
ISSN: 0305-4470
Field of Research (FOR): 010299 Applied Mathematics not elsewhere classified
Peer Reviewed: Yes
HERDC Category Description: C1 Refereed Article in a Scholarly Journal
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