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, \(D = \frac{1}{i } \nabla_x\), 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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Saitō, Y., Umeda, T. The Asymptotic Limits of Zero Modes of Massless Dirac Operators. Lett Math Phys 83, 97–106 (2008). https://doi.org/10.1007/s11005-007-0207-6
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DOI: https://doi.org/10.1007/s11005-007-0207-6