dorsal/arxiv
View SchemaTorus quantization for spinning particles
| Authors | Stefan Keppeler |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0207095 |
| URL | https://arxiv.org/abs/quant-ph/0207095 |
| DOI | 10.1103/PhysRevLett.89.210405 |
| Journal | Phys. Rev. Lett. 89 (2002) 210405 |
Abstract
We derive semiclassical quantization conditions for systems with spin. To this end one has to define the notion of integrability for the corresponding classical system which is given by a combination of the translational motion and classical spin precession. We determine the geometry of the invariant manifolds of this product dynamics which support semiclassical solutions of the wave equation. The semiclassical quantization conditions contain a new term, which is of the same order as the Maslov correction. This term is identified as a rotation angle for a classical spin vector. Applied to the relativistic Kepler problem the procedure sheds some light on the amazing success of Sommerfeld's theory of fine structure [Ann. Phys. (Leipzig) 51 (1916) 1-94].
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"abstract": "We derive semiclassical quantization conditions for systems with spin. To\nthis end one has to define the notion of integrability for the corresponding\nclassical system which is given by a combination of the translational motion\nand classical spin precession. We determine the geometry of the invariant\nmanifolds of this product dynamics which support semiclassical solutions of the\nwave equation. The semiclassical quantization conditions contain a new term,\nwhich is of the same order as the Maslov correction. This term is identified as\na rotation angle for a classical spin vector. Applied to the relativistic\nKepler problem the procedure sheds some light on the amazing success of\nSommerfeld\u0027s theory of fine structure [Ann. Phys. (Leipzig) 51 (1916) 1-94].",
"arxiv_id": "quant-ph/0207095",
"authors": [
"Stefan Keppeler"
],
"categories": [
"quant-ph",
"math-ph",
"math.MP",
"nlin.CD"
],
"doi": "10.1103/PhysRevLett.89.210405",
"journal_ref": "Phys. Rev. Lett. 89 (2002) 210405",
"title": "Torus quantization for spinning particles",
"url": "https://arxiv.org/abs/quant-ph/0207095"
},
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