Scalar potentials, quantum electrodynamics

The accurate quantum mechanical first-principles description of all interactions within a transition-metal cluster represented as a collection of electrons and atomic nuclei is a prerequisite for understanding and predicting such properties. The standard semi-classical theory of the quantum mechanics of electrons and atomic nuclei interacting via electromagnetic waves, i.e., described by Maxwell electrodynamics, turns out to be the theory sufficient to describe all such interactions (21). In semi-classical theory, the motion of the elementary particles of chemistry, i.e., of electrons and nuclei, is described quantum mechanically, while their electromagnetic interactions are described by classical electric and magnetic fields, E and B, often represented in terms of the non-redundant four components of the 4-potential, namely the scalar potential and the vector potential A. 

E. Baum, Vector and Scalar Potentials away from Sources, and Gauge Invariance in Quantum Electrodynamics, Physics Note 3 (1991). 

In previous chapters we considered elementary crystal excitation taking into account only the Coulomb interaction between carriers. From the point of view of quantum electrodynamics (see, for example, (1)) such an interaction is conditioned by an exchange of virtual scalar and longitudinal photons, so that the potential energy, corresponding to this interaction, depends on the carrier positions and not on their velocity distribution. As is well-known, the exchange of virtual transverse photons leads to the so-called retarded interaction between charges. 

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