Maxwell Equations Gaussian Units

In Gaussian units, Jackson [Ref. 7, pp. 220-223] shows that Maxwell s four equations (vacuum form) can first be reduced to a set of two coupled equations... 

The generation of new frequency components from the original frequencies of the incident radiation field can be understood by the use of the Maxwell equations. In Gaussian units, the Maxwell equations can be written as [24] ... 

We start with the Maxwell equations, themselves a concise summary of many experimental observations. In gaussian units these are... 

To construct this limit we can proceed as we did for the nrl of the Dirac equation. We choose a system of units, for which in the Maxwell equations only appears, but not c. There are two allowed choices, either b — c or 6 = 1, but not b = c like in the Gaussian system. 

Maxwell s equations, which were first presented in 1864 and published in 1865 [40], completely describe the classical behavior of electric and magnetic fields and — supported by the Lorentz force law — their interaction with charged particles and currents. In Gaussian units their differential form is given by... 

The macroscopic Maxwell s equations in matter are (in the Gaussian unit system used throughout this handbook) ... 

The governing equations of the electromagnetic field are given by Maxwell s equations (see, for example, Yeh 2005) which in Gaussian units are... 

The above considerations leads to the somewhat troubling question of whether (128) represents the true non-relativistic limit of the Dirac equation in the presence of external fields. Referring back to (110) we have certainly obtained the non-relativistic limit of the free-particle part Lm, but we have in fact retained the interaction term as well as the Lagrangian of the free field. In order to obtain the proper non-relativistic limit, we must consider what is the non-relativistic limit of classical electrodynamics. This task is not facilitated by the fact that, contrary to purely mechanical systems, the laws of electrodynamics appear in different unit systems in which the speed of light appears differently. In the Gaussian system Maxwell s laws are given as... 

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