Effects of superradiance on relativistic Foldy-Wouthuysen densities

• URL: http://arxiv.org/abs/2503.21404v2
• Date: Mon, 09 Jun 2025 21:28:07 GMT
• Title: Effects of superradiance on relativistic Foldy-Wouthuysen densities
• Abstract summary: We investigate wavepacket dynamics for the Klein-Gordon equation.<n>We find that the density based on a Foldy-Wouthuysen transformation of the wavefunction can be locally amplified outside the light-cone.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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