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This paper presents a rigorous theoretical derivation of the causal formation of long-range magnetic fields within quantum electrodynamics, distinguishing non-equilibrium expanding states from standard magnetostatic configurations. The study highlights fundamental differences in energy, photon number, and fluctuations between these regimes, offering new insights into quantum field dynamics under instantaneous current switching.
Expanding quantum magnetic field
arXiv:2605.27426v2 Announce Type: replace Abstract: We develop the quantum theory of the causal formation of a long-range magnetic field generated by an external current that is instantaneously switched on and subsequently kept constant in time. The resulting non-equilibrium quantum state, describing the expanding magnetic field, is obtained exactly and compared with the corresponding quantum magnetostatic state. In contrast to the magnetostatic case, the expanding solution exhibits a propagating shockwave-like front separating regions where the magnetic field has already been formed from those that remain causally disconnected from the source. We show that although the expanding field locally approaches the magnetostatic field behind the shockwave-like front, the associated quantum systems remain distinct at all times. In particular, we obtain manifestly different results for the energy, photon number, and their fluctuations in expanding and magnetostatic field configurations. Our results are first derived for a general external current and then illustrated with a specific example.
Abstract:We develop the quantum theory of the causal formation of a long-range magnetic field generated by an external current that is instantaneously switched on and subsequently kept constant in time. The resulting non-equilibrium quantum state, describing the expanding magnetic field, is obtained exactly and compared with the corresponding quantum magnetostatic state. In contrast to the magnetostatic case, the expanding solution exhibits a propagating shockwave-like front separating regions where the magnetic field has already been formed from those that remain causally disconnected from the source. We show that although the expanding field locally approaches the magnetostatic field behind the shockwave-like front, the associated quantum systems remain distinct at all times. In particular, we obtain manifestly different results for the energy, photon number, and their fluctuations in expanding and magnetostatic field configurations. Our results are first derived for a general external current and then illustrated with a specific example.
arXiv:2605.27426 [quant-ph]
(or arXiv:2605.27426v2 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2605.27426 Focus to learn more arXiv-issued DOI via DataCite
Nucl. Phys. B 1032, 117676 (2026)
https://doi.org/10.1016/j.nuclphysb.2026.117676 Focus to learn more DOI(s) linking to related resources
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Full text under the publisher's open licence · 252 words
