Journal of Operator Theory

Volume 37, Issue 1, Winter 1997 pp. 183-194.

Anticommutativity of spin 1/2 Schrödinger operators with magnetic fields

Authors: Osamu Ogurisu
Author institution:Department of Mathematics, Faculty of Science, Hokkaido University, Sapporo 060, JAPAN

Summary: It is proven that the spin 1/2 Schrödinger operator $\tilde H$ with a constant magnetic field is the square of a sum of mutually strongly anticommuting self-adjoint operators. As an application, by using this formula, the essential spectrum of $\tilde H$ with a vector potential in a class is identified. The class contains a vector potential to which Shigekawa’s theorem (I. Shigekawa, J. Funct. Anal. 101(1991), 255-285) cannot be applied.

Keywords: Anticommutativity, Schrödinger operator, Dirac operator, spin 1/2, essential spectrum, magnetic field.

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