Side jump and anomalous Lorentz transformation of a coherent Dirac wave packet
Abstract
Spin-orbit coupling makes the mean position of a spinning particle transform anomalously under a Lorentz boost, with an additional shift known as a side jump. In this work, we develop a trace method to derive an exact but compact transformation kernel for the probability center of a general three-dimensional Dirac wave packet under an arbitrary finite Lorentz boost. The expression includes the physics of finite momentum width, spin-momentum correlations, and coherent phase structure without a semi-classical expansion. We identify texture-dependent side jumps even at fixed initial mean momentum, spin, and orbital angular momentum, as well as a non-monotonic mass dependence for Gaussian packets at fixed momentum width. The explicit kernels further resolve the spin and orbital angular-momentum contributions for massive and massless fermions, providing a kinematic basis for covariant particle-based spin transport that retains wave-packet information.
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BibTeX
@misc{wu2026side,
title = {{Side jump and anomalous Lorentz transformation of a coherent Dirac wave packet}},
author = {Jin-Rui Wu and Shuai Y. F. Liu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36416},
eprint = {2610.36416},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36416},
}
RIS
TY - UNPB
TI - Side jump and anomalous Lorentz transformation of a coherent Dirac wave packet
AU - Jin-Rui Wu
AU - Shuai Y. F. Liu
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.36416
UR - https://arxiv.org/abs/2610.36416
AB - Spin-orbit coupling makes the mean position of a spinning particle transform anomalously under a Lorentz boost, with an additional shift known as a side jump. In this work, we develop a trace method to derive an exact but compact transformation kernel for the probability center of a general three-dimensional Dirac wave packet under an arbitrary finite Lorentz boost. The expression includes the physics of finite momentum width, spin-momentum correlations, and coherent phase structure without a semi-classical expansion. We identify texture-dependent side jumps even at fixed initial mean momentum, spin, and orbital angular momentum, as well as a non-monotonic mass dependence for Gaussian packets at fixed momentum width. The explicit kernels further resolve the spin and orbital angular-momentum contributions for massive and massless fermions, providing a kinematic basis for covariant particle-based spin transport that retains wave-packet information.
ER -