00-130 A.A. Balinsky and W.D. Evans

On the zero modes of Pauli operators (209K, Postscript) Mar 28, 00

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Abstract. Two results are proved for $\mathrm{nul} \ \mathbb{P}_A$, the dimension of the kernel of the Pauli operator $\mathbb{P}_A = \bigl\{ \bbf{\sigma} \cdotp \bigl(\frac{1}{i} \bbf{\nabla} + \vec{A} \bigr) \bigr\} ^2 $ in $[L^2 (\mathbb{R}^3)]^2$: (i) for $|\vec{B}| \in L^{3/2} (\mathbb{R}^3),$ where $\vec{B} = \mathrm{curl} \vec{A}$ is the magnetic field, $\mathrm{nul} \ \mathbb{P}_{tA} = 0$ except for a finite number of values of $t$ in any compact subset of $(0, \infty)$; (ii) \ $\bigl\{ \ \vec{B}: \ \mathrm{nul} \ \mathbb{P}_{ A} = 0, \ \ | \vec{B} | \in L^{3/2}(\mathbb{R}^3) \ \bigr\} $ contains an open dense subset of $[L^{3/2}(\mathbb{R}^3)]^3$.

Files: 00-130.src( 00-130.keywords , zero_modex.ps )