Plane density of induced vacuum charge in a supercritical Coulomb potential

An expression for the density of a planar induced vacuum charge is obtained in a strong Coulomb potential in coordinate space. Treatment is based on a self-adjoint extension approach for constructing of the Green's function of a charged fermion in this potential. Induced vacuum charge density is calculated and analyzed at the subcritical and supercritical Coulomb potentials for massless and massive fermions. The behavior of the obtained vacuum charge density is investigated at long and short distances from the Coulomb center. The induced vacuum charge has a screening sign. Screening of a Coulomb impurity in graphene is briefly discussed. We calculate the real vacuum polarization charge density that acquires the quantum electrodynamics vacuum in the supercritical Coulomb potential due to the so-called real vacuum polarization. It is shown that the vacuum charge densities essentially differ in massive and massless cases. We expect that our results can, as a matter of principle, be tested in graphene with a supercritical Coulomb impurity.Comment: 12 pages. arXiv admin note: substantial text overlap with arXiv:1601.0766

Polarization operator in the 2+1 dimensional quantum electrodynamics with a nonzero fermion density in a constant uniform magnetic field

The polarization operator (tensor) for planar charged fermions in constant uniform magnetic field is calculated in the one-loop approximation of the 2+1 dimensional quantum electrodynamics (QED$_{2+1}$) with a nonzero fermion density. We construct the Green function of the Dirac equation with a constant uniform external magnetic field in the QED$_{2+1}$ at the finite chemical potential, find the imaginary part of this Green function and then obtain the polarization tensor related to the combined contribution from real particles occupying the finite number of energy levels and magnetic field. We expect that some physical effects under consideration seem to be likely to be revealed in a monolayer graphene sample in the presence of external constant uniform magnetic field $B$ perpendicular to it.Comment: 9 pages, 2 references are delete

A case report of simultaneous mini-invasive treatment of a patient with kidney tumor and tumor thrombus in inferior vena cava

Nowadays, there is a tendency in surgery to use more minimally invasive surgical procedures to decrease the risk of intra- and postoperative complications and to reach a faster rehabilitation period. We report a case of successful simultaneous minimally invasive treatment of a patient with kidney tumor. According to ultrasound examination data, the patient had a tumor in the right kidney. A computed tomography scan of the abdomen verified the tumor and detected a thrombus in the inferior vena cava lumen. Embolization of the right renal artery was performed as the first stage in the hybrid operating room. Right-side nephrectomy and thrombectomy from inferior vena cava, as the second stage, were done by using a robotic surgical system. The feature of this case is that embolization and nephrectomy were simultaneously performed during one surgical procedure. On the 10th day, the patient was discharged from the hospital without any signs of deterioration and complications. Thus, the unique work of two surgical teams proficient in mini-invasive technologies allowed to eliminate tumors and tumor thrombi in a single procedure and to reduce the bleeding, in-hospital stay, and rehabilitation period. This method will help more patients with kidney tumors in the future