Quantum Effects in the Interaction between Electrons and High-Frequency Fields. Vacuum Fluctuation Phenomena

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Abstract
A calculation of dispersion caused by vacuum fluctuations in the velocity of an electron passing through a cavity, when performed by conventional methods, leads to a divergent result. This divergence is due to first-order coupling between electron and free-space radiation field. A unitary transformation is used to eliminate this coupling and still retain first-order coupling with a radiation field which differs from the free-space field, since the latter coupling is needed to discuss electron interaction with a cavity. With the transformed Hamiltonian, equations of motion are derived, and from these, the expectation value of the velocity increment and the dispersion of velocity are obtained. The former is the same as that obtained with the conventional Hamiltonian, but the latter is now given by a convergent result.