dorsal/arxiv
View SchemaEffective Hamiltonians with Relativistic Corrections II: Application to Compton Scattering by a Proton
| Authors | S. Scherer, G. I. Poulis, H. W. Fearing |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9302015 |
| URL | https://arxiv.org/abs/nucl-th/9302015 |
| DOI | 10.1016/0375-9474(94)90079-5 |
| Journal | Nucl.Phys. A570 (1994) 686-700 |
Abstract
We discuss two different methods of obtaining ``effective $2 \times 2$ Hamiltonians'' of the electromagnetic interaction which include relativistic corrections. One is the standard Foldy--Wouthuysen transformation which we compare with the Hamiltonian obtained from a direct reduction of the matrix element of the interaction Hamiltonian between positive--energy solutions of the free Dirac equation. The two approaches are applied to Compton scattering by a proton for which a low--energy theorem exists. It is found that the Foldy--Wouthuysen Hamiltonian yields the same result as a covariant calculation. This is not true for the direct reduction method which will in general lead to incorrect results even after restoring the gauge invariance property of the Hamiltonian. Furthermore, it is shown that an identification of the Z--diagrams of the usual Dirac representation with the contact graphs of the Foldy--Wouthuysen representation is incorrect beyond the order of the low--energy theorem.
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"abstract": "We discuss two different methods of obtaining ``effective $2 \\times 2$\nHamiltonians\u0027\u0027 of the electromagnetic interaction which include relativistic\ncorrections. One is the standard Foldy--Wouthuysen transformation which we\ncompare with the Hamiltonian obtained from a direct reduction of the matrix\nelement of the interaction Hamiltonian between positive--energy solutions of\nthe free Dirac equation. The two approaches are applied to Compton scattering\nby a proton for which a low--energy theorem exists. It is found that the\nFoldy--Wouthuysen Hamiltonian yields the same result as a covariant\ncalculation. This is not true for the direct reduction method which will in\ngeneral lead to incorrect results even after restoring the gauge invariance\nproperty of the Hamiltonian. Furthermore, it is shown that an identification of\nthe Z--diagrams of the usual Dirac representation with the contact graphs of\nthe Foldy--Wouthuysen representation is incorrect beyond the order of the\nlow--energy theorem.",
"arxiv_id": "nucl-th/9302015",
"authors": [
"S. Scherer",
"G. I. Poulis",
"H. W. Fearing"
],
"categories": [
"nucl-th",
"hep-ph"
],
"doi": "10.1016/0375-9474(94)90079-5",
"journal_ref": "Nucl.Phys. A570 (1994) 686-700",
"title": "Effective Hamiltonians with Relativistic Corrections II: Application to Compton Scattering by a Proton",
"url": "https://arxiv.org/abs/nucl-th/9302015"
},
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