Side jump and anomalous Lorentz transformation of a coherent Dirac wave packet

Jin-Rui Wu; Shuai Y. F. Liu

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arXiv · 2610.36416

Side jump and anomalous Lorentz transformation of a coherent Dirac wave packet

Jin-Rui Wu·Shuai Y. F. Liu

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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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Jin-Rui Wu, Shuai Y. F. Liu. 2026-10-26. Side jump and anomalous Lorentz transformation of a coherent Dirac wave packet. https://arxiv.org/abs/2610.36416

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