Electromagnetic field energy density

In die presence of an electromagnetic field of energy of about our systems can undergo absorjDtive transitions from to E2, extracting a photon from die electric field. In addition, as described by Einstein, die field can induce emission of photons from 2 lo E (given E2 is occupied). Let die energy density of die external field be E(v) dren. 

The density of ions and electrons increases quickly in the argon gas, at the same time increasing their kinetic energies as they are pulled back and forth in the applied electromagnetic field and undergo frequent collisions with neutral gas atoms. Some recombination of ions and electrons also occurs to form neutrals. 

This effect resembles the traditional Casimir effect, which describes the attraction between two parallel metallic mirrors in vacuum. Here, however, the fluctuating (bosonic) electromagnetic fields are replaced by fermionic matter fields. Furthermore, the Casimir energy is inferred from the geometry-dependent part of the density of states, and its sign is not fixed, but oscillates according to the relative arrangement and distances of the cavities. 

In the absence of electromagnetic and gluonic fields the free energy density F of a homogeneous color superconducting phase near Tc is [10, 17]... 

We discussed in Section 4.3 the electromagnetic normal modes, or virtual modes, of a sphere, which are resonant when the denominators of the scattering coefficients an and bn are minima (strictly speaking, when they vanish, but they only do so for complex frequencies or, equivalently, complex size parameters). But ext is an infinite series in an and bn, so ripple structure in extinction must be associated with these modes. The coefficient cn (dn) of the internal field has the same denominator as bn(an). Therefore, the energy density, and hence energy absorption, inside the sphere peaks at each resonance there is ripple structure in absorption as well as scattering. 

When considering the energy density of the form (17), it is sometimes convenient to divide the electromagnetic field into two parts when dealing with charge and current distributions that are limited to a region in space near the origin. This implies that the potentials are written as... 

To see this, let us introduce some definitions first. The Poynting vector G represents energy flux density (units esu2cm-3 s-1 = ergcm2s 1). It is a capability of the electromagnetic field to perform work defined as... 

All we need to do is to estimate the average of the potential. To do this, the form of the electric and magnetic fields are used in the normalized energy density of the electromagnetic field... 

At present the density effect has been quite thoroughly studied both theoretically and experimentally. There are different ways of obtaining the calculation formulas for Se. In particular, we can make allowance for the effect the surrounding medium has on the electromagnetic field of a particle by making the substitution c2—c2/e(a>) in the formula for the relativistic differential cross section of energy and momentum transfer... 

This paper presents an account of the dynamics of electric charges coupled to electromagnetic fields. The main approximation is to use non-relativistic forms for the charge and current density. A quantum theory requires either a Lagrangian or a Hamiltonian formulation of the dynamics in atomic and molecular physics the latter is almost universal so the main thrust of the paper is the development of a general Hamiltonian. It is this Hamiltonian that provides the basis for a recent demonstration that the S-matrix on the energy shell is gauge-invariant to all orders of perturbation theory. 

The procedure, known as second quantization, developed as an essential first step in the formulation of quantum statistical mechanics, which, as in the Boltzmann version, is based on the interaction between particles. In the Schrodinger picture the only particle-like structures are associated with waves in 3N-dimensional configuration space. In the Heisenberg picture particles appear by assumption. Recall, that in order to substantiate the reality of photons, it was necessary to quantize the electromagnetic field as an infinite number of harmonic oscillators. By the same device, quantization of the scalar r/>-field, defined in configuration space, produces an equivalent description of an infinite number of particles in 3-dimensional space [35, 36]. The assumed symmetry of the sub-space in three dimensions decides whether these particles are bosons or fermions. The crucial point is that, with their number indeterminate, the particles cannot be considered individuals [37], but rather as intuitively understandable 3-dimensional waves - (Born) -with a continuous density of energy and momentum - (Heisenberg). 

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