Implications for the Description of Atoms and Molecules

All interactions relevant for chemistry are perfectly described by this theory or its generalization to electroweak interactions. However, the solution of its equations of motion (7.30) and (7.31) or even the much simpler calculation of stationary ground states or energy expectation values is far out of reach for all systems under investigation by chemistry. Even today, calculations explicitly taking account of low-order QED effects are difficult for an atom with more than a few electrons [156-158]. 

However, the energies necessary for pair-creation processes are orders of magnitude larger than the energy scale relevant to chemistry and the molecular sciences. Hence, QED is the fundamental theory of chemistry describing 

Moreover, employing the techniques of second quantization prohibits the direct interpretation of the field operators ip as usual quantum mechanical wave functions, since superpositions of states with variable numbers of particles are not compatible with the simple probabilistic interpretation of the wave function. In order to restore this feature, it has become the standard procedure of quantum chemistry to return to a first quantized formulation based on suitable generalizations of the original Dirac equation Eq. (7.9), which will be the subject of the next chapter. 

Our introduction to quantum electrodynamics has been kept rather brief. The reason for this decision is the fact that, although it is the fundamental theory for molecular science, a semi-classical version (chapter 8), in which the electromagnetic fields are not considered quantized, has turned out to be a suitable quantum theory for chemistry. Therefore, we simply provide for further study an extensive list of references to excellent books on quantum electrod)mamics instead. While the first two books consider the results of the theory from an interpretive point of view, the subsequent volumes present the theory in all technical detail. 

Teller, [162]. An Interpretive Introduction to Quantum Field Theory. 

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