We investigate the influence of the vacuum fluctuations of a background electric field over a charged test particle in the presence of a perfectly reflecting flat wall. A switching function connecting different stages of the system is implemented in such a way that its functional dependence is determined by the ratio between the measuring time and the switching duration. The dispersions of the velocity components of the particle are found to be smooth functions of time, and have maximum magnitudes for a measuring time corresponding to about one round trip of a light signal between the particle and the wall. Typical divergences reported in the literature and linked with an oversimplification in modeling this system are naturally regularized in our approach. Estimates suggest that this sort of manifestation of quantum vacuum fluctuations over the motion of the particle could be tested in laboratories.

We investigate some aspects of the Maxwell-Chern-Simons electrodynamics focusing on physical effects produced by the presence of stationary sources and a perfectly conducting plate (mirror). Specifically, in addition to point charges, we propose two new types of point-like sources called topological source and Dirac point, and we also consider physical effects in various configurations that involve them. We show that the Dirac point is the source of the vortex field configurations. The propagator of the gauge field due to the presence of a conducting plate and the interaction forces between the plate and point-like sources are computed. It is shown that the image method is valid for the point-like charges as well as for Dirac points. For the topological source we show that the image method is not valid and the symmetry of spatial refection on the mirror is broken. In all setups considered, it is shown that the topological source leads to the emergence of torques.PACS numbers: I. INTRODUCTIONPlanar models in Quantum Field Theory have several interesting features, both theoretical and experimental. We can mention, for instance, the change in the fermions behavior in comparison with the standard classical and quantum electrodynamics [1]. One of the most important class of models of this kind is the so called Maxwell-Chern-Simons electrodynamics [2], or Abelian topological massive gauge theory [3], which is relevant because it is simultaneously massive and gauge invariant. Theoretical aspects of Maxwell-Chern-Simons electrodynamics have been investigated in Casimir effect [4][5][6][7][8][9], quantum dissipation of harmonic systems [10], quantum electrodynamics (QED 3 ) [11-15], dynamical mass generation [16,17], condensed matter physics (see, for instance, Ref.[24] and references therein), description of graphene properties [18][19][20][21][22][23], noncommutativity [25-28], strings theory [29], dynamics of vortices [30,31], and with a planar boundary [32][33][34][35][36], to mention just a few. In fact, there is a vast literature concerning this model.There is also a generalization of the Chern-Simos electrodynamics in 3 + 1 dimensions, the so called Carroll-Field-Jackiw model [37], which exhibits Lorentz symmetry breaking and whose corresponding electrostatics and magnetostatics has been studied thoroughly in reference [38], as well as the Casimir Effect, in references [39,40]. Another coupling involving the dual gauge field strength tensor in 3 + 1 dimensions is the so called axion θ-electrodynamics, which can be used to describe insulators with boundaries [41][42][43][44].In the context of Casimir Effect, in 3 + 1 dimensions, Chern-Simons surfaces can also be used to obtain Casimir repulsion setups with planar symmetry [45]. In higher dimensions, the Casimir force has been studied in Randall-Sundrum models [46], which can be interpreted as a kind of ground state for Chern-Simons gravity [47].Regarding the Maxwell-Chern-Simons electrodynamics, there are two interesting questions no yet explored in the literature, ...

We study a model for quantum lightcone fluctuations in which vacuum fluctuations of the electric field and of the squared electric field in a nonlinear dielectric material produce variations in the flight times of probe pulses. When this material has a non-zero third order polarizability, the flight time variations arise from squared electric field fluctuations, and are analogous to effects expected when the stress tensor of a quantized field drives passive spacetime geometry fluctuations. We also discuss the dependence of the squared electric field fluctuations upon the geometry of the material, which in turn determines a sampling function for averaging the squared electric field along the path of the pulse. This allows us to estimate the probability of especially large fluctuations, which is a measure of the probability distribution for quantum stress tensor fluctuations.

The contribution from quantum vacuum fluctuations of a real massless scalar field to the motion of a test particle that interacts with the field in the presence of a perfectly reflecting flat boundary is here investigated. There is no quantum induced dispersions on the motion of the particle when it is alone in the empty space. However, when a reflecting wall is introduced, dispersions occur with magnitude dependent on how fast the system evolves between the two scenarios. A possible way of implementing this process would be by means of an idealized sudden switching, for which the transition occurs instantaneously. Although the sudden process is a simple and mathematically convenient idealization it brings some divergences to the results, particularly at a time corresponding to a round trip of a light signal between the particle and the wall. It is shown that the use of smooth switching functions, besides regularizing such divergences, enables us to better understand the behavior of the quantum dispersions induced on the motion of the particle. Furthermore, the action of modifying the vacuum state of the system leads to a change in the particle energy that depends on how fast the transition between these states is implemented. Possible implications of these results to the similar case of an electric charge near a perfectly conducting wall are discussed.