Power-Zienau-Woolley representations of nonrelativistic QED for atoms and molecules
The interaction terms in the general nonrelativistic Hamiltonian for a collection of spin-free charged particles and the electromagnetic field may be expressed in terms of so-called polarization fields. The general Hamiltonian is related to the familiar Coulomb gauge theory by a family of formally u...
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| Format: | Article |
| Language: | English |
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American Physical Society
2020-02-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.2.013206 |
| _version_ | 1797211532511150080 |
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| author | R. Guy Woolley |
| author_facet | R. Guy Woolley |
| author_sort | R. Guy Woolley |
| collection | DOAJ |
| description | The interaction terms in the general nonrelativistic Hamiltonian for a collection of spin-free charged particles and the electromagnetic field may be expressed in terms of so-called polarization fields. The general Hamiltonian is related to the familiar Coulomb gauge theory by a family of formally unitary transformations with a line integral over the Coulomb gauge vector potential as generator. The particular choice of a straight-line path starting at an arbitrary origin and ending at a charge defines the Power-Zienau-Woolley transformation; it is commonly approximated by a truncated multipole expansion of the integral about the arbitrary origin. The transformation may be analyzed as a certain kind of coherent state displacement. For an overall neutral many-particle system the paths using the arbitrary origin can be eliminated in favor of paths with end points at the positions of oppositely charged particles. The paths may be interpreted as lines of force in the sense of Faraday, while the polarization fields are just the electromagnetic field strengths for the specified line of force. We develop this line integral representation for the polarization fields and calculate the self-energy of the electric polarization field P using a straight-line path. For an overall neutral pair of point charges, the energy contributions are their individual (infinite) self-energies, a contact interaction, and a divergent pair term. which together replace the familiar Coulomb interaction. Of course one must not forget also the coupling between P and the transverse electric field; the paradox is resolved by the requirement for gauge invariance. These results mirror findings in the relatively remote area of high-energy physics where the pairs of oppositely charged particles are typically quark-antiquark partners, and similar line integrals giving the same singular interaction are used. |
| first_indexed | 2024-04-24T10:27:59Z |
| format | Article |
| id | doaj.art-62318a914c5e46b1a2d8d367da18bbcd |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:27:59Z |
| publishDate | 2020-02-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-62318a914c5e46b1a2d8d367da18bbcd2024-04-12T16:50:19ZengAmerican Physical SocietyPhysical Review Research2643-15642020-02-012101320610.1103/PhysRevResearch.2.013206Power-Zienau-Woolley representations of nonrelativistic QED for atoms and moleculesR. Guy WoolleyThe interaction terms in the general nonrelativistic Hamiltonian for a collection of spin-free charged particles and the electromagnetic field may be expressed in terms of so-called polarization fields. The general Hamiltonian is related to the familiar Coulomb gauge theory by a family of formally unitary transformations with a line integral over the Coulomb gauge vector potential as generator. The particular choice of a straight-line path starting at an arbitrary origin and ending at a charge defines the Power-Zienau-Woolley transformation; it is commonly approximated by a truncated multipole expansion of the integral about the arbitrary origin. The transformation may be analyzed as a certain kind of coherent state displacement. For an overall neutral many-particle system the paths using the arbitrary origin can be eliminated in favor of paths with end points at the positions of oppositely charged particles. The paths may be interpreted as lines of force in the sense of Faraday, while the polarization fields are just the electromagnetic field strengths for the specified line of force. We develop this line integral representation for the polarization fields and calculate the self-energy of the electric polarization field P using a straight-line path. For an overall neutral pair of point charges, the energy contributions are their individual (infinite) self-energies, a contact interaction, and a divergent pair term. which together replace the familiar Coulomb interaction. Of course one must not forget also the coupling between P and the transverse electric field; the paradox is resolved by the requirement for gauge invariance. These results mirror findings in the relatively remote area of high-energy physics where the pairs of oppositely charged particles are typically quark-antiquark partners, and similar line integrals giving the same singular interaction are used.http://doi.org/10.1103/PhysRevResearch.2.013206 |
| spellingShingle | R. Guy Woolley Power-Zienau-Woolley representations of nonrelativistic QED for atoms and molecules Physical Review Research |
| title | Power-Zienau-Woolley representations of nonrelativistic QED for atoms and molecules |
| title_full | Power-Zienau-Woolley representations of nonrelativistic QED for atoms and molecules |
| title_fullStr | Power-Zienau-Woolley representations of nonrelativistic QED for atoms and molecules |
| title_full_unstemmed | Power-Zienau-Woolley representations of nonrelativistic QED for atoms and molecules |
| title_short | Power-Zienau-Woolley representations of nonrelativistic QED for atoms and molecules |
| title_sort | power zienau woolley representations of nonrelativistic qed for atoms and molecules |
| url | http://doi.org/10.1103/PhysRevResearch.2.013206 |
| work_keys_str_mv | AT rguywoolley powerzienauwoolleyrepresentationsofnonrelativisticqedforatomsandmolecules |