The Zero Modes and the Zero Resonances of Dirac Operators
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چکیده
The zero modes and the zero resonances of the Dirac operator H = α · D + Q(x) are discussed, where α = (α1, α2, α3) is the triple of 4× 4 Dirac matrices, D = 1 i ∇x, and Q(x) = ` qjk(x) ́ is a 4× 4 Hermitian matrix-valued function with |qjk(x)| ≤ C〈x〉, ρ > 1. We shall show that every zero mode f(x) is continuous on R and decays at infinity with the decay rate |x| if 1 < ρ < 3, |x| log |x| if ρ = 3, and |x| if ρ > 3. Also, we shall show that H has no zero resonance if ρ > 5/2.
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تاریخ انتشار 2006