Effects of superradiance on relativistic Foldy-Wouthuysen densities
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915358001070080 |
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| author | Daem, F. Matzkin, A. |
| author_facet | Daem, F. Matzkin, A. |
| contents | Recent interest in the studies of structured states obtained in relativistic electron beams has highlighted the use of two alternative descriptions, each based on a different wavefunction and the related space-time density. Although both wavefunctions obey the Dirac equation (one directly and the other through a Foldy-Wouthuysen transformation) they lead to different dynamics and properties, such as the presence or absence of spin-orbit interactions. In this work we investigate wavepacket dynamics for the Klein-Gordon equation, which displays the same ambiguity regarding the choice of different densities, in a setting involving Klein tunneling across a series of supercritical potential barriers. Relying on the superradiant character of this setting, we obtain solutions to the wavepacket dynamics indicating that the density based on a Foldy-Wouthuysen transformation of the wavefunction can be locally amplified outside the light-cone. In principle, the exponential increase of the charge due to the field inhomogeneities can lead to an arbitrarily large amplification over macroscopic distances. These results question the interpretation of the Foldy-Wouthuysen density as a fundamentally correct probability or charge density. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21404 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Effects of superradiance on relativistic Foldy-Wouthuysen densities Daem, F. Matzkin, A. Quantum Physics High Energy Physics - Phenomenology High Energy Physics - Theory Recent interest in the studies of structured states obtained in relativistic electron beams has highlighted the use of two alternative descriptions, each based on a different wavefunction and the related space-time density. Although both wavefunctions obey the Dirac equation (one directly and the other through a Foldy-Wouthuysen transformation) they lead to different dynamics and properties, such as the presence or absence of spin-orbit interactions. In this work we investigate wavepacket dynamics for the Klein-Gordon equation, which displays the same ambiguity regarding the choice of different densities, in a setting involving Klein tunneling across a series of supercritical potential barriers. Relying on the superradiant character of this setting, we obtain solutions to the wavepacket dynamics indicating that the density based on a Foldy-Wouthuysen transformation of the wavefunction can be locally amplified outside the light-cone. In principle, the exponential increase of the charge due to the field inhomogeneities can lead to an arbitrarily large amplification over macroscopic distances. These results question the interpretation of the Foldy-Wouthuysen density as a fundamentally correct probability or charge density. |
| title | Effects of superradiance on relativistic Foldy-Wouthuysen densities |
| topic | Quantum Physics High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2503.21404 |