The Asymptotic Limits of Zero Modes of Massless Dirac Operators |
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Authors: | Yoshimi Saitō Tomio Umeda |
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Institution: | (1) Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL 35294, USA;(2) Department of Mathematical Science, University of Hyogo, Shosha, Himeji 671-2280, Japan |
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Abstract: | Asymptotic behaviors of zero modes of the massless Dirac operator H = α · D + Q(x) are discussed, where α = (α1, α2, α3) is the triple of 4 × 4 Dirac matrices, , and Q(x) = (q
jk
(x)) is a 4 × 4 Hermitian matrix-valued function with | q
jk
(x) | ≤ C 〈x〉−ρ, ρ > 1. We shall show that for every zero mode f, the asymptotic limit of |x|2
f (x) as |x| → + ∞ exists. The limit is expressed in terms of the Dirac matrices and an integral of Q(x) f (x).
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Keywords: | Dirac operators Weyl– Dirac operators Zero modes Asymptotic limits |
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