Consistency of Loop Regularization Method and Divergence Structure of QFTs Beyond One-Loop Order

We study the problem how to deal with tensor-type two-loop integrals in the Loop Regularization (LORE) scheme. We use the two-loop photon vacuum polarization in the massless Quantum Electrodynamics (QED) as the example to present the general procedure. In the processes, we find a new divergence structure: the regulated result for each two-loop diagram contains a gauge-violating quadratic harmful divergent term even combined with their corresponding counterterm insertion diagrams. Only when we sum up over all the relevant diagrams do these quadratic harmful divergences cancel, recovering the gauge invariance and locality.Comment: 33 pages, 5 figures, Sub-section IIIE removed, to be published in EPJ

Proposed neutron interferometry test of Berry's phase for a circulating planar spin

The energy eigenstates of a spin$-\frac{1}{2}$ particle in a magnetic field confined to a plane, define a planar spin. If the particle moves adiabatically around a loop in this plane, it picks up a topological Berry phase that can only be an integer multiple of $\pi$. We propose a neutron interferometry test of the Berry phase for a circulating planar spin induced by a magnetic field caused by a very long current-carrying straight wire perpendicular to the plane. This Berry phase causes destructive interference in the direction of the incoming beam of thermal neutrons moving through a triple-Laue interferometer

Exponential Stability of the Inhomogeneous Navier-Stokes-Vlasov System in Vacuum

The main purpose of the present paper is to study the influence of the vacuum on the asymptotic behaviors of solutions to the inhomogeneous Navier-Stokes-Vlasov system in $\mathbb{R}^3\times\mathbb{R}^3$. To this end, we establish the uniform bound of the macroscopic density associated with the distribution function and prove the global existence and uniqueness of strong solutions to the Cauchy problem with vacuum for either small initial energy or large viscosity coefficient. The uniform boundedness and the presence of vacuum enable us to show that as the time evolves, the fluid velocity decays, while the distribution function concentrates towards a Dirac measure in velocity centred at $0$, with an exponential rate

Tris(5,6-dimethyl-1H-benzimidazole-κN 3)(pyridine-2,6-dicarboxyl­ato-κ3 O 2,N,O 6)nickel(II)

The title mononuclear complex, [Ni(C7H3NO4)(C9H10N2)3], shows a central NiII atom which is coordinated by two carboxyl­ate O atoms and the N atom from a pyridine-2,6-dicarboxyl­ate ligand and by three N atoms from different 5,6-dimethyl-1H-­benzimidazole ligands in a distorted octa­hedral geometry. The crystal structure shows intermolecular N—H⋯O hydrogen bonds

Tris(1H-benzimidazole-κN 3)(pyridine-2,6-dicarb­oxy­lato-κ3 O 2,N,O 6)nickel(II)

In the title complex, [Ni(C7H3NO4)(C7H6N2)3], the NiII ion is coordinated by two carboxyl­ate O atoms and the N atom from a pyridine-2,6-dicarboxyl­ate ligand and by three N atoms from three benzimidazole ligands to form a slightly distorted octa­hedral geometry. In the crystal, mol­ecules are linked by N—H⋯O hydrogen bonds to form a three-dimensional network