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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



The stochastic mechanics of the Pauli equation

Author: Timothy C. Wallstrom
Journal: Trans. Amer. Math. Soc. 318 (1990), 749-762
MSC: Primary 81P20; Secondary 60J65
MathSciNet review: 986033
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Abstract: In stochastic mechanics, the Bopp-Haag-Dankel diffusions on $ {\mathbb{R}^3} \times \operatorname{SO} (3)$ are used to represent particles with spin. Bopp and Haag showed that in the limit as the particle's moment of inertia $ I$ goes to zero, the solutions of the Bopp-Haag equations converge to that of the regular Pauli equation. Nelson has conjectured that in the same limit, the projections of the Bopp-Haag-Dankel diffusions onto $ {\mathbb{R}^3}$ converge to a Markovian limit process. In this paper, we prove this conjecture for spin $ \operatorname{spin} \;\tfrac{1} {2}$ and regular potentials, and identify the limit process as the diffusion naturally associated with the solution to the regular Pauli equation.

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Keywords: Stochastic mechanics, spin diffusions, Bopp-Haag, Dankel, Pauli equation
Article copyright: © Copyright 1990 American Mathematical Society

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