We consider the problem of self-adjoint extension of Hamilton operators for charged quantum particles in the pure Aharonov-Bohm potential (infinitely thin solenoid). We present a pragmatic approach to the problem based on the orthogonalization of the radial solutions for different quantum numbers. Then we discuss a model of a scalar particle with a magnetic moment which allows to explain why the self-adjoint extension contains arbitrary parameters and give a physical interpretation.

We investigate the scattering of an electron by an infinitely thin and infinitely long straight magnetic flux tube in the framework of QED. We discuss the solutions of the Dirac and Maxwell fields in the related external pure AB potential and evaluate matrix elements and differential probabilities for the bremsstrahlung process. The dependence of the resulting cross section on the energy, direction and polarization of the involved particles is analyzed. In the low energy regime a surprising angular asymmetry is found which results from the interaction of the electron's magnetic moment with the magnetic field.

We evaluate the cross section for electron-positron pair production by a single high energy photon in the space-time of a static, straight cosmic string. Energy and momentum conservation precludes this process in empty Minkowski space. It happens around a cosmic string, in spite of the local flatness of the metric, as a consequence of the conical structure of space. Previous results based on a simplified model with scalar fields are here extended to the realistic QED case. Analytic expressions are found in three different regimes: near the threshold, at energies much larger than the electron rest mass M, and at ultrahigh energies, much larger than M/δ, with δ the string mass per unit length in Planck units.

We study the influence of static gravitational fields on the spontaneous emission and the Lamb shift of atoms. To illustrate the procedure we consider a two-level atom coupled by a dipole interaction to a massless scalar quantum field in a general static Riemann space and work out the Einstein coefficient and the radiative energy shift. To treat an example, the general scheme is applied to a cosmic string spacetime. The possibility is discussed to detect, at least in principle, the cosmic string via the modified spontaneous emission. PACS number(s): 42.50.-p, 04.62.+v, 98.80.Cq I. I N T R O D U C T I O NIt is well known that the decay rate for spontaneous emission, and accordingly the respective Einstein coefficient, is not a n inherent property of the atom but depends on the particular vacuum in which the atom is located. Similarly the shift of the atom's energy level, the Lamb shift, depends on the surroundings. In a confined space, for example, realized by a cavity, for mirrors causing boundary conditions and in dielectric media the mode structure of the electromagnetic field is modified as compared to the empty Minkowski space. Consequently, the decay rate and Lamb shift differ from their free-space values. These values refer to atoms a t rest or in uniform motion. For accelerated atoms, spontaneous excitation and radiative energy shifts have been worked out in [l] and [2] with the intention to analyze quantitatively the distinct contribution of vacuum fluctuations and radiation reaction.The basis of all the considerations mentioned above was a flat spacetime. The inclusion of the influence of inhomogeneous gravitational fields amounts to the transition to a curved Riemann space. In the following we restrict ourselves t o static gravitational fields or spacetimes, respectively. We will give a general discussion of the spontaneous decay and Lamb shift in this physical situation. An important application could be found in the astrophysical context where the Einstein coefficient is modified for example in the strong gravitational field of collapsed stars. This modification enters the interpretation of the spectroscopical data.Below we will study a simpler application of our general scheme in choosing as static Riemann space the spacetime of a straight cosmic string which is flat everywhere outside the string but shows a conical topology. This demonstrates how a nontrivial topology influences spontaneous emission and Lamb shift. A cosmic string could, only in principle, of course, be sensed this way. 'Electronic address:We shall consider a model consisting of a two-level atom and a scalar quantum field interacting via a coupling of dipole type. The more realistic calculation based on a n electromagnetic vector potential would follow the same lines. We are interested in the total amount of considered effects only. Therefore, we do not discuss the contributions of vacuum fluctuations and radiation reaction separately.The structure of the paper is as follows. In Sec. I1 we quantize in the canonical way a Klein-Gor...

In the framework of QED we evaluate the cross section for electron-positron pair production by a single photon in the presence of the external Aharonov-Bohm potential in first order of perturbation theory. We analyse energy, angular and polarization distributions at different energy regimes: near the threshold and at high photon energies.Comment: LaTeX file, 13 page