Lorentz interaction

M. Rambaut and J. P. Vigier, Ampere forces considered as collective non-relativistic limit of the sum of all Lorentz interactions acting on individual current elements Possible consequences for electromagnetic discharge stability and Tokamak behavior, Phys. Lett. A 148(5), 229-238 (1990). 

The parameters in simple potential models for interactions between unlike molecules A and B are often deduced from tlie corresponding parameters for the A-A and B-B interactions using combination mles . For example, the a and e parameters are often estimated from the Lorentz-Berthelot mles ... 

The Coulomb gauge theory and the Lorentz gauge theory thus both describe the same physical phenomena, but they handle one aspect of the physical situation, namely, the Coulomb interaction, in fundamentally different ways. In the Coulomb gauge the interaction is... 

Incorporated into the electron field, while in the Lorentz gauge it appears as being caused by the emission and absorption of longitudinal quanta. It is because the Coulomb interaction does not involve observable quanta that this freedom of choosing the gauge exists. 

Similar considerations lead to the transformation properties of the one-photon states and of the photon in -operators which create photons of definite momentum and helicity. We shall, however, omit them here. Suffice it to remark that the above transformation properties imply that the interaction hamiltonian density Jf mAz) = transforms like a scalar under restricted inhomogeneous Lorentz transformation... 

The Ether is not useful to teach MT. The EM field is most effectively viewed as an irreducible entity completely defined by Maxwell s equations. (If one wants to make the interaction with point charges in N.M or QM explicit, one can add the Lorentz force or the minimal coupling.) All physical properties of th EM field and its interaction with matter follow from Maxwell s equations and the matter equations. 

Landman, U., and W. D. Luedtke, Consequences of tip-sample interactions, in Scanning Tunneling Microscopy III, R. Wiesendanger and H. J. Guntherodt Eds., Springer-Verlag, Berlin, 1993. Lorentz, W. J., and W. Plieth, Eds., Electrochemical Nanotechnology, Wiley-VCH, New York, 1996. 

It is important to notice that in Equation 10.11, only the sum of the three terms is Lorentz invariant. The first term corresponds to the interaction of the charge density with the external Coulomb potential and the last term can be written in the form... 

The above reasoning has led to the fireball internal-external shocks model. This model is rather independent of the nature of the central engine. The latter one is just required to produce highly relativistic outflow, either in the form of kinetic energy or as Poynting flux. The radiation is produced in (collisionless) shocks. These can either occur due to interaction of the outflow with the cir-cumstellar material ( external shocks ) or due to interactions of different portions of the outflow with different Lorentz-factors, so-called internal shocks . 

In Chapter 4 we will consider the so-called classical approximation, in which the electromagnetic radiation is considered as a classical electromagnetic wave and the solid is described as a continnous medium, characterized by its relative dielectric constant e or its magnetic permeability fx. The interaction will then be described by the classical oscillator (the Lorentz oscillator). 

The most simple, but general, model to describe the interaction of optical radiation with solids is a classical model, due to Lorentz, in which it is assumed that the valence electrons are bound to specific atoms in the solid by harmonic forces. These harmonic forces are the Coulomb forces that tend to restore the valence electrons into specific orbits around the atomic nuclei. Therefore, the solid is considered as a collection of atomic oscillators, each one with its characteristic natural frequency. We presume that if we excite one of these atomic oscillators with its natural frequency (the resonance frequency), a resonant process will be produced. From the quantum viewpoint, these frequencies correspond to those needed to produce valence band to conduction band transitions. In the first approach we consider only a unique resonant frequency, >o in other words, the solid consists of a collection of equivalent atomic oscillators. In this approach, coq would correspond to the gap frequency. 

Let us now analyze the interaction of a light wave with our collection of oscillators at frequency two- In this case, the general motion of a valence electron bound to a nucleus is a damped oscillator, which is forced by the oscillating electric field of the light wave. This atomic oscillator is called a Lorentz oscillator. The motion of such a valence electron is then described by the following differential equation ... 

Because of the long-range nature of the dipolar interaction, care must be taken in the evaluation of the dipolar field. For hnite systems the sums in Eq. (3.12) are performed over all particles in the system. Eor systems with periodic boundary conditions the Ewald method [57-59], can be used to correctly calculate the conditionally convergent sum involved. However, in most work [12,13] the simpler Lorentz-cavity method is used instead. 

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