Random Motion Of A Charged Test Particle With A Constant Classical Velocity In A Spacetime With A Plane Boundary

In classical physics, vacuum is regarded as having nothing. However, in quantum mechanics and quantum field theory, the vacuum state is considered as a state in which there does not exist any particle or any mode of quantum field and it is physically a state of lowest energy. Although the number of particles is zero in vacuum, some other properties of particles may still be present and exhibit certain quantum uncertainties. This is reflected in the fact that the vacuum expectation value of the field squared is nonzero in quantum field theory. Therefore there exist the so called vacuum fluctuations. In the QED, for example, there exist the effects of zero-point (vacuum) oscillations of photons, the effects of vacuum polarization of electron-positron paris, and so on. They all could result in observable consequences , such as the anomalous magnetic moment of the electron, the spontaneous emission of atoms in excited states, the Lamb shift and the Casimir effect, which have been verfied in experiments. Recently, Yu and Ford have studied the electromagnetic vacuum fluctuations and the Brownian motion of a charged test particle near a reflecting boundary. They have calculated the mean squared fluctuations in both the position and the velocity of the test particles.This thesis is organised as follows. In the first chapter, we give a brief review of some concepts of quantum vacuum fluctuations, their effects and their experimental verifications. At the same time, we also introduce the notion of the Brownian motion of charged test particles caused by vacuum fluctuations. In the second chapter, we present a brief overview of the results obtained in the literature in the study of the Brownion motion of charged test particles driven by vacuum fluctuations and the methods used. In the third chapter, the core part of the thesis, we study the random motion of a charged test particle coupled to electromagnetic vacuum fluctuatings near a perfectly reflecting plane boundary with a nonzero classical constant veolcity in a direction parallel to the plane. We calculate the mean squared fluctuations in the velocity and position of the test particle taking into account both fluctuating electric and magnetic forces, Our results show that the influance of fluctuating magnetic fields is, in general, of the higher order than that caused by fluctuating electric fields and is thus negliable.Finally, we will conclude with a summary of our work and an outlook for possible future research.