Brownian Motion of a Test Particle with a Normal Classical Velocity in Spacetime with a Plane Boundary

We study the random motion of a charged test particle with a normal classical constant velocity in a spacetime with a perfectly reflecting plane boundary and calculate both the velocity and position dispersions of the test particle. Our results show that the dispersions in the normal direction are weakened while those in the parallel directions are strengthened as compared to the classical static case when the test particle classically moves away from the boundary. However, if the classical motion reverses its direction, then the dispersions in the normal direction are reinforced while those in the parallel directions get weakened.

Spontaneous Emission of an Inertial Multi-Level Atom in a Spacetime with a Reflecting Plane Boundary

We calculate the contributions of the vacuum fluctuations and radiation reaction to the rate of change of the mean atomic energy for a multi-level hydrogen atom in the multipolar coupling scheme in a spacetime with a reflecting boundary. Our results show that, due to the presence of the boundary, the polarizations of the atom in the parallel direction and in the normal direction are weighted differently in terms of their contributions to the spontaneous emission rate, which is an oscillating function of the atom distance from the boundary. The possible experimental implications of our result are briefly discussed.

Relic Gravitational Waves and Trans-Planckian Physics

Assuming that the effects of trans-Planckian physics are encoded in the choice of initial conditions, mode by mode, for vacuum states at the time when its wavelength becomes equal to the scale of new physics （Planck＇s scale for example）, we calculate the spectrum of energy densities of total relic gravitational waves from de Sitter inflation to the matter dominated universe. Our results show that the spectrum acquires corrections due to the consideration of trans-Planckian physics and these corrections depend sensitively on the vacuum state that was actually realized at the beginning of the inflation.

Radiation Rate of a Two-Level Atom in a Spacetime with a Reflecting Boundary

We study a two-level atom in interaction with a real massless scalar quantum field in a spacetime with a reflecting boundary. We calculate the rate of change of the atomic energy for the atom. The presence of the boundary modifies the quantum fluctuations of the scalar field, which in turn modifies the rate of change of the atomic energy. It is found that the modifications induced by the presence of a boundary make the spontaneous radiation rate of an excited atom to oscillate near the boundary and this oscillatory behaviour may offer a possible opportunity for experimental tests for geometrical （boundary） effects in flat spacetime.

Radiative Energy Shifts of an Accelerated Multilevel Atom Coupled to the Derivative of a Scalar Field

We study the energy level shifts of an accelerated multilevel atom in dipole coupling to the derivative of a quantum massless scalar field and separately calculate the contributions of vacuum fluctuations and radiation reaction to the shifts. It is found that, in contrast to the case of a monopole-like interaction, both the vacuum fluctuations and radiation reaction contributions are changed by acceleration, and they all contain non-thermal correction terms. Our results suggest that the effect of acceleration on the energy shifts is dependent on the type of the interaction between the atom and the quantum field.

Casimir Force at a Finite Cut-Off

We calculate the Casimir force at a finite cut-off A by summing the forces induced by the all fluctuation modes. We show that the Casimir force is independent of the cut-off function in the limit L∧ → ∞. There is a correction in the order of （L∧）^-2, when L∧ is finite and large. This correction becomes remarkable when L is comparable with the microscopic length scale ∧^-1. It has been demonstrated that the Casimir force at a finite cut-off should be defined by summing forces of all fluctuation modes, instead of the derivative of Casimir energy with respect to L where an additional derivative of the cut-off function has been introduced.

Renormalizability and nonrenormalizable interactions

Arguments are provided which show that extension of renormalizability in quantum field theory is possible. By an appropriate choice of effective Lagrangian, a dressed Feynman propagator is obtained. In this scheme, higher order Feynman diagrams become self-convergent and nonrenormalizable interactions become renormalizable. As an example, the vacuum fluctuation effects on ρ meson mass for the vector-tensor coupling model is discussed. It is found that the result can agree with the experimental value when coupling constant is adjusted.

Relative Energy Shift of a Two-Level Atom in a Cylindrical Spacetime

We investigate the evolution dynamics of a two-level atom system interacting with the massless scalar field in a Cylindrical spacetime. We find that both the energy shifts of ground state and excited state can be separated into two parts due to the vacuum fluctuations. One is the corresponding energy shift for a rest atom in four-dimensional Minkowski space without spatial compactification, the other is just the modification of the spatial compactified periodic length. It will reveal that the influence of the presence of one spatial compactified dimension can not be neglected in Lamb shift as the relative energy level shift of an ~tom.