Electromagnetic theory angular momentum

Several theories have been developed to explain the rainbow phenomena, including the Lorenz-Mie theory, Airy s theory, the complex angular momentum theory that provides an approximation to the Lorenz-Mie theory, and the theory based on Huy gen s principle. Among these theories, only the Lorenz-Mie theory provides an exact solution for the scattering of electromagnetic waves by a spherical particle. The implementation of the rainbow thermometry for droplet temperature measurement necessitates two functional relationships. One relates the rainbow angle to the droplet refractive index and size, and the other describes the dependence of the refractive index on temperature of the liquid of interest. The former can be calculated on the basis of the Lorenz-Mie theory, whereas the latter may be either found in reference handbooks/literature or calibrated in laboratory. 

This is due to the comparative weakness of the electromagnetic interaction, the theory of which contains a small dimensionless parameter (fine structure constant), by the powers of which the corresponding quantities can be expanded. The electron transition probability of the radiation of one photon, characterized by a definite value of angular momentum, in the first order of quantum-electrodynamical perturbation theory mdy be described as follows [53] (a.u.) ... 

The metric coefficient in the theory of gravitation [110] is locally diagonal, but in order to develop a metric for vacuum electromagnetism, the antisymmetry of the field must be considered. The electromagnetic field tensor on the U(l) level is an angular momentum tensor in four dimensions, made up of rotation and boost generators of the Poincare group. An ordinary axial vector in three-dimensional space can always be expressed as the sum of cross-products of unit vectors... 

It can be shown by a simple extension of the wave equation to include electromagnetic phenomena (a subject which will not be discussed in this book) that the magnetic moment associated with the orbital motion of an electron is obtained from the orbital angular momentum by multiplication by the factor e/2m0c, just as in the classical and old quantum theory (Sec. Id). The component of orbital magnetic moment along the 2 axis is... 

It will be shown that the Dirac equation for the tree electron m an external electromagnetic field is leading to the spin concept. Thus, in relativistic theory, the spin angular momentum spears in a natural way, whereas in the non-relativistic formalism, it was the subject of a postulate of quantum mechanics (p. 26). 

The Dirac equation for a particle in the electromagnetic field contains the interaction of the spin magnetic moment with the magnetic field. In this way, spin angular momentum appears in the Dirac theory in a natural way (as opposed to the non-relativistic case, where it has had to be postulated . 

In his doctoral dissertation de Broglie postulated that particles such as the electron, proton, etc. should also possess wave-like properties in exact analogy with the particle-like properties exhibited by electromagnetic waves in the quantum theory of radiation. For motion in one dimension he postulated that the momentum of the particle p and its kinetic energy E were related to the wavevector k and angular frequency w of the guiding wave, I, by the relations... 

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