scholarly journals Optical Helicity and Chirality: Conservation and Sources

2019 ◽  
Vol 9 (5) ◽  
pp. 828 ◽  
Author(s):  
Frances Crimin ◽  
Neel Mackinnon ◽  
Jörg Götte ◽  
Stephen Barnett
Keyword(s):  
Electromagnetic Field ◽  
Free Space ◽  
Density Operator ◽  
Continuity Equation ◽  
Symmetry Transformation ◽  
Dual Symmetry ◽  
Free Electromagnetic Field

We consider the helicity and chirality of the free electromagnetic field, and advocate the former as a means of characterising the interaction of chiral light with matter. This is in view of the intuitive quantum form of the helicity density operator, and of the dual symmetry transformation generated by its conservation. We go on to review the form of the helicity density and its associated continuity equation in free space, in the presence of local currents and charges, and upon interaction with bulk media, leading to characterisation of both microscopic and macroscopic sources of helicity.

Simulations of electric field at the initiation altitudes of sprites and halos generated by the thundercloud charge structure and lightning channels of causative return strokes

2021 ◽  
Author(s):  
Petr Kaspar ◽  
Ivana Kolmasova ◽  
Ondrej Santolik ◽  
Martin Popek ◽  
Pavel Spurny ◽  
...  
Keyword(s):  
Electromagnetic Field ◽  
Electric Field ◽  
Boundary Conditions ◽  
Free Space ◽  
Nonlinear Effects ◽  
Charge Structure ◽  
Transient Luminous Events ◽  
Lightning Channel ◽  
Free Parameters

<p><span>Sprites and halos are transient luminous events occurring above thunderclouds. They can be observed simultaneously or they can also appear individually. Circumstances leading to initiation of these events are still not completely understood. In order to clarify the role of lightning channels of causative lightning return strokes and the corresponding thundercloud charge structure, we have developed a new model of electric field amplitudes at halo/sprite altitudes. It consists of electrostatic and inductive components of the electromagnetic field generated by the lightning channel in free space at a height of 15 km. Above this altitude we solve Maxwell’s equations self-consistently including the nonlinear effects of heating and ionization/attachment of the electrons. At the same time, we investigate the role of a development of the thundercloud charge structure and related induced charges above the thundercloud. We show how these charges lead to the different distributions of the electric field at the initiation heights of the halos and sprites. We adjust free parameters of the model using observations of halos and sprites at the Nydek TLE observatory and using measurements of luminosity curves of the corresponding return strokes measured by an array of fast photometers. The latter measurements are also used to set the boundary conditions of the model.</span></p>

scholarly journals Some arguments for the wave equation in Quantum theory

2021 ◽  
Vol 5 (1) ◽  
pp. 314-336
Author(s):  
Tristram de Piro ◽  
Keyword(s):  
Electromagnetic Field ◽  
Wave Equation ◽  
Quantum Theory ◽  
Continuity Equation ◽  
Wave Equations ◽  
Maxwell's Equations ◽  
Atomic System ◽  
Balmer Series ◽  
Inertial Frames ◽  
The Stability

We clarify some arguments concerning Jefimenko’s equations, as a way of constructing solutions to Maxwell’s equations, for charge and current satisfying the continuity equation. We then isolate a condition on non-radiation in all inertial frames, which is intuitively reasonable for the stability of an atomic system, and prove that the condition is equivalent to the charge and current satisfying certain relations, including the wave equations. Finally, we prove that with these relations, the energy in the electromagnetic field is quantised and displays the properties of the Balmer series.

Quantisation of the Electromagnetic Field and Spontaneous Photon Emission

2021 ◽  
pp. 4-23
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Electromagnetic Field ◽  
Excited State ◽  
Physical Interpretation ◽  
Gauge Invariance ◽  
Photon Emission ◽  
Perturbation Expansion ◽  
Atomic State ◽  
Abstract Concepts ◽  
Free Electromagnetic Field ◽  
Physical Result

We develop the method of canonical quantisation for the case of the free electromagnetic field. We choose the Coulomb gauge, which has a simpler physical interpretation. We introduce the creation and annihilation operators in this framework. The formalism is applied to the problem of spontaneous emission of radiation from an excited atomic state at first order in the perturbation expansion. This allows us to obtain a concrete physical result, namely the computation of an excited state decay rate, and, at the same time, have a first look at abstract concepts, such as gauge invariance and renormalisation.

Canonical Quantization of the Classical Hamiltonian for a Relativistic Spin-0 Particle

1991 ◽  
Vol 46 (11) ◽  
pp. 933-938
Author(s):  
H.-J. Briegel ◽  
B.-G. Englert ◽  
G. Süssmann
Keyword(s):  
Density Operator ◽  
Continuity Equation ◽  
Canonical Quantization ◽  
Relativistic Invariance ◽  
Relativistic Spin

AbstractWhen quantizing the classical Hamiltonian H (q,p,t) = [m2c4 + (c p - e A(t,q))2]1/2 + e V(t, q), commutators of the form [f (a), g(b)], where [a,b] is not a c-number, have to be evaluated. The concept of continuously symmetrized products enables us to derive a number of statements, such as a continuity equation for the density operator δ{q(t)-x)=n(t, x), in a formally concise way. We can also show, then, that the dependence of the Hamiltonian on higher powers of the kinetic momentum destroys the relativistic invariance of the theory, even if we admit a more general coupling of the external potentials than above.

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