Asymptotic freedom, dimensional transmutation, and an infrared conformal fixed point for the δ-function potential in one-dimensional relativistic quantum mechanics

We consider the Schrödinger equation for a relativistic point particle in an external one-dimensional δ-function potential. Using dimensional regularization, we investigate both bound and scattering states, and we obtain results that are consistent with the abstract mathematical theory of self-adjoint extensions of the pseudodifferential operator H=p2+m2−−−−−−−√. Interestingly, this relatively simple system is asymptotically free. In the massless limit, it undergoes dimensional transmutation and it possesses an infrared conformal fixed point. Thus it can be used to illustrate nontrivial concepts of quantum field theory in the simpler framework of relativistic quantum mechanics.

On vertical electric fields at lunar magnetic anomalies

We study the interaction between a magnetic dipole mimicking the Gerasimovich magnetic anomaly on the lunar surface and the solar wind in a self-consistent 3-D quasi-neutral hybrid simulation where ions are modeled as particles and electrons as a charge-neutralizing fluid. Especially, we consider the origin of the recently observed electric potentials at lunar magnetic anomalies. An antimoonward Hall electric field forms in our simulation resulting in a potential difference of <300V on the lunar surface, in which the value is similar to observations. Since the hybrid model assumes charge neutrality, our results suggest that the electric potentials at lunar magnetic anomalies can be formed by decoupling of ion and electron motion even without charge separation.

Solution of the relativistic Schrödinger equation for the δ ′ -Function potential in one dimension using cutoff regularization

We study the relativistic version of the Schrödinger equation for a point particle in one dimension with the potential of the first derivative of the delta function. The momentum cutoff regularization is used to study the bound state and scattering states. The initial calculations show that the reciprocal of the bare coupling constant is ultraviolet divergent, and the resultant expression cannot be renormalized in the usual sense, where the divergent terms can just be omitted. Therefore, a general procedure has been developed to derive different physical properties of the system. The procedure is used first in the nonrelativistic case for the purpose of clarification and comparisons. For the relativistic case, the results show that this system behaves exactly like the delta function potential, which means that this system also shares features with quantum filed theories, like being asymptotically free. In addition, in the massless limit, it undergoes dimensional transmutation, and it possesses an infrared conformal fixed point. The comparison of the solution with the relativistic delta function potential solution shows evidence of universality.

New fully kinetic model for the study of electric potential, plasma, and dust above lunar landscapes

We have developed a new fully kinetic electrostatic simulation, HYBes, to study how the lunar landscape affects the electric potential and plasma distributions near the surface and the properties of lifted dust. The model embodies new techniques that can be used in various types of physical environments and situations. We demonstrate the applicability of the new model in a situation involving three charged particle species, which are solar wind electrons and protons, and lunar photoelectrons. Properties of dust are studied with test particle simulations by using the electric fields derived from the HYBes model. Simulations show the high importance of the plasma and the electric potential near the surface. For comparison, the electric potential gradients near the landscapes with feature sizes of the order of the Debye length are much larger than those near a flat surface at different solar zenith angles. Furthermore, dust test particle simulations indicate that the landscape relief influences the dust location over the surface. The study suggests that the local landscape has to be taken into account when the distributions of plasma and dust above lunar surface are studied. The HYBes model can be applied not only at the Moon but also on a wide range of airless planetary objects such as Mercury, other planetary moons, asteroids, and nonactive comets.