Lorentz condition

In the expression (9-514), k0 = k so that in fact / ( ) is only a function ofk. In Eq. (9-514) the integration is carried out over the positive light cone. Clearly the so defined L x) will satisfy the wave equation (9-510). In order for this %u(x) to satisfy the Lorentz condition a k) must be such that... 

Lorentz approximation, 46 Lorentz condition, 551 Lorentz gauge, 657,664 Lorentz group homogeneous, 490... 

Appendix A The Lorentz Condition Appendix B Electron Model of Present Theory B.l. General Equations of the Equilibrium State The Charged-Particle State... 

In terms of 0(3) covariant derivatives, Evans et al. [78] have shown that the Proca-type equation represented by the form (22) can be derived without imposing the conventional Lorentz condition L = 0. This result is supported by the following two considerations. 

When the two square brackets in the right-hand member of Eq. (A.3) both transform as 4-vectors, their scalar product becomes invariant in spacetime. The quantity L is then equal to an arbitrary constant. Consequently the terms containing L in Eqs. (A.l) and (A.2) vanish regardless whether the Lorentz condition L = 0 is being satisfied. 

J. P. Vigier et al., Classical electrodynamics without the Lorentz condition Extracting energy from the vacuum, Physica Scripta 61(5), 513-517 (2000). 

To remove arbitariness, one can also select these two potentials to satisfy the Lorentz condition ... 

The free electromagnetic waves have the transverse polarization. The longitudinal and scalar polarization are introduced in Eq(54) artificially and should vanish in the expression for any observable. This can be achieved by imposing the Lorentz condition (40). Then the contributions of the longitudinal and scalar polarizations cancel in the expressions (42), (43) for the field strength and for the energy of electromagnetic field ... 

Actually none of the simple suppositions as to the nature of the effective field appear to be really adequate, although the Lorentz condition E = E + (4 r/3) P seems to have become hallowed with time, even if not with experiment. Hence in what follows, faute de mieux, we shall stick to the simplest, if unrealistic, assumption of identifying E with E unless it be specifically stated otherwise. This procedure will also have the virtue of keeping the expressions as simple as possible during the discussions which follow. If afterwards one wishes to take into account the consequences of... 

We start by considering a one-electron system influenced by an electromagnetic field. In a source-free region this field can be expressed by the magnetic vector potential A, fulfilling the condition V-A = 0 according to the Lorentz condition V-A+c" 9 /5t = 0. The Hamiltonian of the system is... 

This condition is called the Lorentz condition and defines the Lorentz gauge. Using this condition in (3.19) provides us finally with a set of decoupled equations ... 

Because and j are invariant, it follows that the four-vector potential A is also Lorentz invariant. Note that this is really implied in the Lorentz condition (3.23), which is a product of the Lorentz-invariant four-gradient and the four-vector A and can be written... 

From the Lorentz condition in the Fourier space we have ... 

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