The late-time tail behaviors of massive scalar fields are examined analytically in the background of a black hole with a global monopole. It is found that the presence of a solid deficit angle in the background metric makes the massive scalar fields decay faster in the intermediate times. However, the asymptotically late-time tail is not affected and it has the same decay rate of t25/6 as in the Schwarzschild and nearly extreme Reissner-Nordstrom backgrounds.

Using the methods developed by Fewster and colleagues, we derive a quantum inequality for the free massive spin- 3 2 Rarita-Schwinger fields in four dimensional Minkowski spacetime. Our quantum inequality bound for the Rarita-Schwinger fields is weaker, by a factor of 2, than that for the spin- 1 2 Dirac fields. This fact along with other quantum inequalities obtained by various other authors for the fields of integer spin (bosonic fields) using similar methods lead us to conjecture that, in flat spacetime, separately for bosonic and fermionic fields, the quantum inequality bound gets weaker as the number of degrees of freedom of the field increases. A plausible physical reason might be that the more field degrees of freedom, the more freedom one has to create negative energy, therefore the weaker the quantum inequality bound.

The Brownian motion of a charged test particle caused by quantum electromagnetic vacuum fluctuations between two perfectly conducting plates is examined and the mean squared fluctuations in the velocity and position of the test particle are calculated. Our results show that the Brownian motion in the direction normal to the plates is reinforced in comparison to that in the single plate case. The effective temperature associated with this normal Brownian motion could be three times as large as that in the single plate case. However, the negative dispersions for the velocity and position in the longitudinal directions, which could be interpreted as reducing the quantum uncertainties of the particle, acquire positive corrections due to the presence of the second plate, and are thus weakened.

We study the Brownian motion of a charged test particle coupled to electromagnetic vacuum fluctuations near a perfectly reflecting plane boundary. The presence of the boundary modifies the quantum fluctuations of the electric field, which in turn modifies the motion of the test particle. We calculate the resulting mean squared fluctuations in the velocity and position of the test particle. In the case of directions transverse to the boundary, the results are negative. This can be interpreted as reducing the quantum uncertainty which would otherwise be present.

Quantum fluctuations of the light cone are examined in a four-dimensional spacetime with two parallel planes. Both the Dirichlet and the Neumann boundary conditions are considered. In all the cases we have studied, quantum light cone fluctuations are greater where the Neumann boundary conditions are imposed, suggesting that quantum light cone fluctuations depend not only on the geometry and topology of the spacetime as has been argued elsewhere but also on boundary conditions. Our results also show that quantum light cone fluctuations are larger here than that in the case of a single plane. Therefore the confinement of gravitons in a smaller region by the presence of a second plane reinforces the quantum fluctuations and this can be understood as a consequence of the uncertainty principle.