On the Fast Electrons-Optical Modes Interaction Problem Error
Abstract
A recently developed relativistic quantum optics approach for a fast electron beam-optical modes interaction problem (Optica 6, 1524--1534 (2019)) contains suggestion about a smallness of the error induced by replacement Ψk⃗≈Ψk⃗0 for noninteracting free electron Dirac spinors at such wave vector k⃗ that |k⃗−k⃗0 | ≪|k⃗0| with k⃗0 as a peaked wave vector of a focused electron beam. Here, based on quantum information approach we strictly investigated a degree of coincidence of spinors Ψk⃗ and Ψk⃗0 by calculating fidelity for them. The analytical expression is obtained. It is shown that the fidelity inevitably depends on not only wave vectors k⃗ and k⃗0 but also on mutual orientation of [k⃗0,k⃗] and s⃗̂†σ⃗s⃗̂ with s⃗ is a two-component spin unit vector and σ⃗ is a vector of Pauli matrices. This result can be conceived as a chirality-like effect in the fidelity and constraints spin arbitrariness when applying the developed relativistic quantum optics approach to the problems of interest. A geometrical configuration of k⃗0, k⃗−k⃗0, and s⃗̂†σ⃗s⃗̂ that is optimal in terms of fidelity is established.
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BibTeX
@misc{churochkina2026fast,
title = {{On the Fast Electrons-Optical Modes Interaction Problem Error}},
author = {Svetlana Churochkina and Dmitry Churochkin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13976},
eprint = {2610.13976},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13976},
}
RIS
TY - UNPB
TI - On the Fast Electrons-Optical Modes Interaction Problem Error
AU - Svetlana Churochkina
AU - Dmitry Churochkin
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.13976
UR - https://arxiv.org/abs/2610.13976
AB - A recently developed relativistic quantum optics approach for a fast electron beam-optical modes interaction problem (Optica 6, 1524--1534 (2019)) contains suggestion about a smallness of the error induced by replacement Ψ_k⃗≈Ψ_k⃗_0 for noninteracting free electron Dirac spinors at such wave vector k⃗ that |k⃗−k⃗_0 | ≪|k⃗_0| with k⃗_0 as a peaked wave vector of a focused electron beam. Here, based on quantum information approach we strictly investigated a degree of coincidence of spinors Ψ_k⃗ and Ψ_k⃗_0 by calculating fidelity for them. The analytical expression is obtained. It is shown that the fidelity inevitably depends on not only wave vectors k⃗ and k⃗_0 but also on mutual orientation of [k⃗_0,k⃗] and s⃗̂^†σ⃗s⃗̂ with s⃗ is a two-component spin unit vector and σ⃗ is a vector of Pauli matrices. This result can be conceived as a chirality-like effect in the fidelity and constraints spin arbitrariness when applying the developed relativistic quantum optics approach to the problems of interest. A geometrical configuration of k⃗_0, k⃗−k⃗_0, and s⃗̂^†σ⃗s⃗̂ that is optimal in terms of fidelity is established.
ER -