Point charge electromagnetic theory

To this point, we have considered only the radiation field. We now turn to the interaction between the matter and the field. According to classical electromagnetic theory, the force on a particle with charge e due to the electric and magnetic fields is... 

It is not possible for conventional electromagnetic models of the electron to explain the observed property of a point charge with an excessively small radial dimension [20]. Nor does the divergence in self-energy of a point charge vanish in quantum field theory where the process of renormalization has been applied to solve the problem. 

These four fundamental equations of electromagnetic theory can be very elegantly expressed in terms of the vector operators divergence and curl. The first Maxwell s equation is a generalization of Coulomb s law for the electric field of a point charge ... 

It was pointed out j n Ref. 64 that the scp.qened electrostatic potential (i.e. V + V, not including any V ) rather than t e self-consistent potential should be used for determination of e -and this holds for other dielectric quantities, as well. In fact, the electromagnetic theory refers to classical test charges, the exchange-correlation effects enter only indirectly, through determination of the actual charge distribution. The screened potential = V ° + V plotted in Fie. 5.1.7 for comparison is... 

The first theoretical model of optical activity was proposed by Drude in 1896. It postulates that charged particles (i.e., electrons), if present in a dissymmetric environment, are constrained to move in a helical path. Optical activity was a physical consequence of the interaction between electromagnetic radiation and the helical electronic field. Early theoretical attempts to combine molecular geometric models, such as the tetrahedral carbon atom, with the physical model of Drude were based on the use of coupled oscillators and molecular polarizabilities to explain optical activity. All subsequent quantum mechanical approaches were, and still are, based on perturbation theory. Most theoretical treatments are really semiclassical because quantum theories require so many simplifications and assumptions that their practical applications are limited to the point that there is still no comprehensive theory that allows for the predetermination of the sign and magnitude of molecular optical activity. 

The key feature of the theory of QED—whether it is cast in nonrelativis-tic or fully covariant forms is that the electromagnetic field obeys quantum mechanical laws. A frequent first step in the construction of either version of the theory is the writing of the classical Lagrangian function for the interaction of a charged particle with a radiation field. For a particle of mass m, electronic charge —e, located at position vector q, and moving with velocity d /df c in a position-dependent potential V( ) subject to electromagnetic radiation described by scalar and vector potentials cp0) and a(r), at field point... 

The quantum theory explains the unique behavior of charged particles that are as small and move as rapidly as electrons. Because of its close relationship to electromagnetic radiation, an appreciation of quantum theory requires an understanding of the following important points related to electromagnetic radiation ... 

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