Divergence charge density

The mathematics is completed by one additional theorem relating the divergence of the gradient of the electrical potential at a given point to the charge density at that point through Poisson s equation... 

The introduction of the current density (3) in 3-space is, in fact, less intuitive than what could appear at first glance. As soon as the charge density (4) is permitted to exist as the result of a nonzero electric field divergence, the Lorentz invariance of a 4-current (7) with the time part namely requires the associated space part to adopt the form (3), that is, by necessity. 

It should be mentioned that in the approach with nonzero electric divergence, the photon mass is also related to the space charges in vacuo. Now, in the approach with a / 0, we have j = ctE but jeff = 0. Let us now assume j = aE and j 7 0, which means fs 0. In such a case, jo is assumed to be associated with p, where p is the charge density in vacuo. So, in such an approach one can think of the existence of a kind of space charge in vacuo that is to be considered to be associated to nonzero electric field divergence. This will result in a displacement current in vacuum similar to that measured by Bartlett and Corle [43]. The assumption of the existence of space charge in vacuo makes our theory not only fully relativistic but also helps us to understand gauge condition. In the conventional framework of Maxwell s equations... 

We regroup those terms in Eq. (6) that are associated with lncs. This is so because In cs diverges as cs approaches zero. Hence, the coefficient of In cs must vanish. This leads to an explicit connection between 0 and the linear charge density [17, 31]... 

Begin with the Poisson equation but keep the e matrix inside the divergence operation V (eV0) = -4jrpext (see Fig. L3.24). The net electric-charge density pext at a given point depends on the magnitude of potential as in Debye-Huckel theory. As before in relation (L3.175),... 

Current density is a measure of the density of flow of a conserved charge. The equation governing the distribution of potential and current flow in electrolyte can be derived from the continuity equation, charge conservation. The divergence of the current density is equal to the negative rate of change of the charge density [6] ... 

Surprising result. However, SOlyom showed that in a single chain if 2g2 > g-j > o the charge density wave (CDW) response is divergent as In the two chain problem... 

For the single chain (w = w2 = 0), there are seven two-particle correlation functions, four of which are divergent. The divergent ones are the CDW (charge-density wave), SDW (spin-density wave), SS (singlet superconductor), and TS (triplet superconductor) response functions and are shown in Fig. (3). The... 

From the fundamental basis of Gauss s law, the divergence of the displacement field -eV< > equals the charge density, or... 

The expectation value (In (r)) is not defined (divergence to —oo), but the moment function M k) can be defined for A = 0, so that M k) =0 for all integer k>0. The Barrett moment for this charge density distribution simply yields zero,... 

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