The Relativistic Stern-Gerlach Force
Abstract
The relativistic Lagrangian for a spinning particle in an electromagnetic field is derived from the known Lagrangian in the particle's rest frame. The resulting relativistic Stern-Gerlach and Thomas precession forces on the particle are then derived from the Lagrangian in the laboratory frame. In particular, the longitudinal component of this combined Stern-Gerlach-Thomas force does not contain a term proportional to gamma-squared as was claimed in a previous derivation [1].
- Publication:
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arXiv e-prints
- Pub Date:
- February 2008
- DOI:
- 10.48550/arXiv.0802.0154
- arXiv:
- arXiv:0802.0154
- Bibcode:
- 2008arXiv0802.0154T
- Keywords:
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- Physics - Accelerator Physics
- E-Print:
- In this revised version of the paper, the Stern-Gerlach component of the canonical momentum is treated as velocity-independent in analogy to the electromagnetic momentum, and its time derivative is simplified by inserting the known time derivative of the spin