dorsal/arxiv
View SchemaThe Covariant Stark Effect
| Authors | M. C. Land, L. P. Howitz |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0103136 |
| URL | https://arxiv.org/abs/quant-ph/0103136 |
| DOI | 10.1023/A:1017516119084 |
| Journal | Found.Phys.31:967-991,2001 |
Abstract
This paper examines the Stark effect, as a first order perturbation of manifestly covariant hydrogen-like bound states. These bound states are solutions to a relativistic Schr\"odinger equation with invariant evolution parameter, and represent mass eigenstates whose eigenvalues correspond to the well-known energy spectrum of the non-relativistic theory. In analogy to the nonrelativistic case, the off-diagonal perturbation leads to a lifting of the degeneracy in the mass spectrum. In the covariant case, not only do the spectral lines split, but they acquire an imaginary part which is lnear in the applied electric field, thus revealing induced bound state decay in first order perturbation theory. This imaginary part results from the coupling of the external field to the non-compact boost generator. In order to recover the conventional first order Stark splitting, we must include a scalar potential term. This term may be understood as a fifth gauge potential, which compensates for dependence of gauge transformations on the invariant evolution parameter.
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"abstract": "This paper examines the Stark effect, as a first order perturbation of\nmanifestly covariant hydrogen-like bound states. These bound states are\nsolutions to a relativistic Schr\\\"odinger equation with invariant evolution\nparameter, and represent mass eigenstates whose eigenvalues correspond to the\nwell-known energy spectrum of the non-relativistic theory. In analogy to the\nnonrelativistic case, the off-diagonal perturbation leads to a lifting of the\ndegeneracy in the mass spectrum. In the covariant case, not only do the\nspectral lines split, but they acquire an imaginary part which is lnear in the\napplied electric field, thus revealing induced bound state decay in first order\nperturbation theory. This imaginary part results from the coupling of the\nexternal field to the non-compact boost generator. In order to recover the\nconventional first order Stark splitting, we must include a scalar potential\nterm. This term may be understood as a fifth gauge potential, which compensates\nfor dependence of gauge transformations on the invariant evolution parameter.",
"arxiv_id": "quant-ph/0103136",
"authors": [
"M. C. Land",
"L. P. Howitz"
],
"categories": [
"quant-ph",
"hep-th",
"math-ph",
"math.MP"
],
"doi": "10.1023/A:1017516119084",
"journal_ref": "Found.Phys.31:967-991,2001",
"title": "The Covariant Stark Effect",
"url": "https://arxiv.org/abs/quant-ph/0103136"
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