Constructing Berry-Maxwell equations with Lorentz invariance and Gauss'
law of Weyl monopoles in 4D energy-momentum space
- URL: http://arxiv.org/abs/2308.00612v1
- Date: Sun, 30 Jul 2023 05:37:50 GMT
- Title: Constructing Berry-Maxwell equations with Lorentz invariance and Gauss'
law of Weyl monopoles in 4D energy-momentum space
- Authors: Yiming Pan, Ruoyu Yin
- Abstract summary: We present the construction of a reciprocal electromagnetic field by extending the Berry curvatures from momentum space into 4D energy-momentum space.
We propose the reciprocal electromagnetic field as a physical reality rooted in the fundamental principles of special relativity and Gauss's law of Weyl monopoles.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We present the construction of a reciprocal electromagnetic field by
extending the Berry curvatures from momentum space 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
governing conventional electromagnetic fields. Furthermore, we demonstrate that
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
Schrodinger equation. Consequently, we propose the reciprocal electromagnetic
field as a physical reality, rooted in the fundamental principles of special
relativity and Gauss's law of Weyl monopoles. To validate our theory
experimentally, we outline three potential effects for verification: (i)
Lorentz boost of a Weyl monopole, (ii) reciprocal Thouless pumping, and (iii)
plane-wave solutions of Berry-Maxwell equations.
Related papers
- Generalized Gouy Rotation of Electron Vortex beams in uniform magnetic fields [54.010858975226945]
We study the dynamics of EVBs in magnetic fields using exact solutions of the relativistic paraxial equation in magnetic fields.
We provide a unified description of different regimes under generalized Gouy rotation, linking the Gouy phase to EVB rotation angles.
This work offers new insights into the dynamics of EVBs in magnetic fields and suggests practical applications in beam manipulation and beam optics of vortex particles.
arXiv Detail & Related papers (2024-07-03T03:29:56Z) - Dirac materials in parallel non-uniform electromagnetic fields generated
by SUSY: A new class of chiral Planar Hall Effect? [0.0]
We find a nontrivial current density in the same plane where the electric and magnetic fields lie, but perpendicular to both of them.
This density is the sum of current densities for the left- and right-chiralities, suggesting that the net current is a consequence of chiral symmetry.
arXiv Detail & Related papers (2023-06-28T17:48:56Z) - Predicting Angular-Momentum Waves Based on Yang-Mills Equations [0.0]
Yang-Mills (YM) theory incorporates Maxwell's equations unifying electromagnetism.
The angular-momentum waves are hopefully realized in the experiments through the oscillations of spin angular momentum.
arXiv Detail & Related papers (2023-04-25T07:50:20Z) - Third quantization of open quantum systems: new dissipative symmetries
and connections to phase-space and Keldysh field theory formulations [77.34726150561087]
We reformulate the technique of third quantization in a way that explicitly connects all three methods.
We first show that our formulation reveals a fundamental dissipative symmetry present in all quadratic bosonic or fermionic Lindbladians.
For bosons, we then show that the Wigner function and the characteristic function can be thought of as ''wavefunctions'' of the density matrix.
arXiv Detail & Related papers (2023-02-27T18:56:40Z) - Physics-constrained 3D Convolutional Neural Networks for Electrodynamics [77.34726150561087]
We create a 3D convolutional PCNN to map time-varying current and charge densities J(r,t) and p(r,t) to vector and scalar potentials A(r,t) and V(r,t)
We generate electromagnetic fields according to Maxwell's equations: B=curl(A), E=-div(V)-dA/dt.
arXiv Detail & Related papers (2023-01-31T15:51:28Z) - Effects of Lorentz Symmetry Breaking Environment on Generalized
Relativistic Quantum Oscillator Field [0.0]
We consider a possible scenario of the Lorentz-Violating effects with a Cornell-type electric field and a linear magnetic field.
We see that the eigenvalue solutions get modified by the Lorentz symmetry-breaking effects in comparison to the Landau levels.
arXiv Detail & Related papers (2022-12-22T13:06:04Z) - Dimensional reduction of the Dirac theory [0.0]
We perform a reduction from three to two spatial dimensions of the physics of a spin-1/2 fermion coupled to the electromagnetic field.
We consider first the free case, in which motion is determined by the Dirac equation, and then the coupling with a dynamical electromagnetic field.
arXiv Detail & Related papers (2022-11-15T23:55:10Z) - Exact quantum-mechanical equations for particle beams [91.3755431537592]
These equations present the exact generalizations of the well-known paraxial equations in optics.
Some basic properties of exact wave eigenfunctions of particle beams have been determined.
arXiv Detail & Related papers (2022-06-29T20:39:36Z) - Construction of Dirac spinors for electron vortex beams in background
electromagnetic fields [0.0]
Exact solutions of the Dirac equation, a system of four partial differential equations, are rare.
Given the growing number of applications of high energy electron beams interacting with a variety of quantum systems in laser fields, novel methods for finding exact solutions to the Dirac equation are called for.
We present a method for building up solutions to the Dirac equation employing a recently introduced approach for the description of spinorial fields and their driving electromagnetic fields in terms of geometric algebras.
arXiv Detail & Related papers (2020-11-25T11:55:37Z) - Dissipative flow equations [62.997667081978825]
We generalize the theory of flow equations to open quantum systems focusing on Lindblad master equations.
We first test our dissipative flow equations on a generic matrix and on a physical problem with a driven-dissipative single fermionic mode.
arXiv Detail & Related papers (2020-07-23T14:47:17Z) - General quantum-mechanical solution for twisted electrons in a uniform
magnetic field [68.8204255655161]
A theory of twisted (and other structured) paraxial electrons in a uniform magnetic field is developed.
The observable effect of a different behavior of relativistic Laguerre-Gauss beams with opposite directions of the orbital angular momentum penetrating from the free space into a magnetic field is predicted.
arXiv Detail & Related papers (2020-05-13T16:35:10Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.