Maxwell's equations in the multipolar representation

Haller, Kurt

doi:10.1103/physreva.26.1796

Cited by 11 publications

(2 citation statements)

References 7 publications

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“…There are various representations of Maxwell equations. Some examples are the following: standard complex representation [1,2], spinor form [3], Silberstein-Bateman-Majorana form [4][5][6], Kemmer-Duffin-Petiau form (also known as the meson algebra) [4,7], matrix representation [8], Dirac form [9][10][11], Poincaré algebra [12], Debye sources [13,14], Penrose's transformation presented in terms of integral geometry [15,16], integral representation [17], and multipolar presentation [18]. This paper uses the complex vector representation of Maxwell equations in order to develop the presented complex operator formalism.…”

Section: Introductionmentioning

confidence: 99%

Complex Symmetric Formulation of Maxwell Equations for Fields and Potentials

Livadiotis

2018

Mathematics

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Maxwell equations have two types of asymmetries between the electric and magnetic fields. The first asymmetry is the inhomogeneity induced by the absence of magnetic charge sources. The second asymmetry is due to parity. We show how both asymmetries are naturally resolved under an alternative formulation of Maxwell equations for fields or potentials that uses a compact complex vector operator representation. The developed complex symmetric operator formalism can be easily applied to performing the continuity equation, the field wave equations, the Maxwell equations for potentials, the gauge transformations, and the 4-momentum representation; in general, the developed formalism constitutes a simple way of unfolding the Maxwell theory. Finally, we provide insights for extending the presented analysis within the context of (i) bicomplex numbers and tessarine algebra; and (ii) L p -spaces in nonlinear Maxwell equations.

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Section: Introductionmentioning

confidence: 99%

Complex Symmetric Formulation of Maxwell Equations for Fields and Potentials

Livadiotis

2018

Mathematics

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“…However, it is shown that the ordinary EM fields and Maxwell's equations become gauge dependent in this method [19]. This inconsistency is extensively studied by different authors [20,21,22]. To overcome this problem, Kobe [18] quantized the EM fields without gauge fixing and redefined the EM fields strength tensor that is invariant under the OGTs.…”

Section: Introductionmentioning

confidence: 99%

Operator Gauge Symmetry in QED

Khademi

Nasiri

2006

SIGMA

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Abstract. In this paper, operator gauge transformation, first introduced by Kobe, is applied to Maxwell's equations and continuity equation in QED. The gauge invariance is satisfied after quantization of electromagnetic fields. Inherent nonlinearity in Maxwell's equations is obtained as a direct result due to the nonlinearity of the operator gauge transformations. The operator gauge invariant Maxwell's equations and corresponding charge conservation are obtained by defining the generalized derivatives of the f irst and second kinds. Conservation laws for the real and virtual charges are obtained too. The additional terms in the field strength tensor are interpreted as electric and magnetic polarization of the vacuum.

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$$\vec A.\vec p or\vec r.\vec E?.$$ Minimal Coupling and Multipolar Hamiltonians in the Quantum Theory of Radiation

Haller

1984

Quantum Electrodynamics and Quantum Optics

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Maxwell's equations in the multipolar representation

Abstract: Arguments are given in support of a remark made by Mandel, that Maxwell's equations are not consistent with the multipolar form of the Hamiltonian for the electromagnetic field interacting with nonrelativistic electrons.

Cited by 11 publications

References 7 publications

Complex Symmetric Formulation of Maxwell Equations for Fields and Potentials

Complex Symmetric Formulation of Maxwell Equations for Fields and Potentials

Operator Gauge Symmetry in QED

$$\vec A.\vec p or\vec r.\vec E?.$$ Minimal Coupling and Multipolar Hamiltonians in the Quantum Theory of Radiation

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