Constructing Berry-Maxwell equations with Lorentz invariance and Gauss' law of Weyl monopoles in 4D energy-momentum space

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Hauptverfasser: Pan, Yiming, Yin, Ruoyu
Format: Preprint
Veröffentlicht: 2023
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author Pan, Yiming
Yin, Ruoyu
author_facet Pan, Yiming
Yin, Ruoyu
contents We present the construction of a reciprocal electromagnetic field by extending the Berry curvatures into four-dimensional (4D) energy-momentum space. The resulting governing equations, termed Berry-Maxwell equations, are derived, by incorporating Lorentz invariance to constrain the parameter space of energy-momentum. Notably, these Berry-Maxwell equations exhibit dual and self-dual structures compared to the Maxwell equations. The very existence of Berry-Maxwell equations is independent of the geometrical phase of matter waves, implying that they cannot be directly derived from the time-dependent Schrödinger equation. Indeed, we find that the physical reality of this reciprocal electromagnetic field is rooted in the fundamental principles of special relativity and Gauss's law of Weyl monopoles. To validate our theory experimentally, we outline three effects for verification: (i) Lorentz boost of a Weyl monopole, (ii) reciprocal Thouless pumping, and (iii) plane-wave solutions of Berry-Maxwell's equations.
format Preprint
id arxiv_https___arxiv_org_abs_2308_00612
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Constructing Berry-Maxwell equations with Lorentz invariance and Gauss' law of Weyl monopoles in 4D energy-momentum space
Pan, Yiming
Yin, Ruoyu
Classical Physics
Optics
Quantum Physics
We present the construction of a reciprocal electromagnetic field by extending the Berry curvatures into four-dimensional (4D) energy-momentum space. The resulting governing equations, termed Berry-Maxwell equations, are derived, by incorporating Lorentz invariance to constrain the parameter space of energy-momentum. Notably, these Berry-Maxwell equations exhibit dual and self-dual structures compared to the Maxwell equations. The very existence of Berry-Maxwell equations is independent of the geometrical phase of matter waves, implying that they cannot be directly derived from the time-dependent Schrödinger equation. Indeed, we find that the physical reality of this reciprocal electromagnetic field is rooted in the fundamental principles of special relativity and Gauss's law of Weyl monopoles. To validate our theory experimentally, we outline three effects for verification: (i) Lorentz boost of a Weyl monopole, (ii) reciprocal Thouless pumping, and (iii) plane-wave solutions of Berry-Maxwell's equations.
title Constructing Berry-Maxwell equations with Lorentz invariance and Gauss' law of Weyl monopoles in 4D energy-momentum space
topic Classical Physics
Optics
Quantum Physics
url https://arxiv.org/abs/2308.00612