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

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

Induced current in the presence of magnetic flux tube of small radius

The induced current density, corresponding to the massless Dirac equation in (2+1) dimensions in a magnetic flux tube of small radius is considered. This problem is important for graphene. In the case, when an electron can not penetrate the region of nonzero magnetic field, this current is the odd periodical function of the magnetic flux. If the region inside the magnetic tube is not forbidden for penetration of electron, the induced current is not a periodical function of the magnetic flux. However in the limit $R\to 0$, where $R$ is the radius of magnetic flux tube, this function has the universal form which is independent of the magnetic field distribution inside the magnetic tube at fixed value of the magnetic flux.Comment: 5 pages, 1 figur

Depolarizing GABA and developmental epilepsies

© 2014 John Wiley & Sons Ltd. Early in development, GABA, which is the main inhibitory neurotransmitter in adult brain, depolarizes immature neurons and exerts dual-excitatory and shunting/inhibitory-effects in the developing neuronal networks. The present review discusses some general questions, including the properties of excitation at depolarizing GABAergic synapse and shunting inhibition by depolarizing GABA; technical issues in exploration of depolarizing GABA using various techniques and preparations, including the developmental aspects of traumatic injury and what is known (or rather unknown) on the actions of GABA in vivo; complex roles of depolarizing GABA in developmental epilepsies, including a contribution of depolarizing GABA to enhanced excitability in the immature networks, caused by repetitive seizures accumulation of intracellular chloride concentration that increases excitatory GABA power and its synchronizing proconvulsive effects, and correction of chloride homeostasis as a potential strategy to treat neonatal seizures

Intracellular blockade of GABA<inf>A</inf> receptors in the rat hippocampal neurons

The intracellular blockade of GABAA-receptor-mediated currents is a useful approach to suppress the GABAergic conductance in a single cell and to isolate the glutamatergic component of network-driven activities. Previously an approach has been described allowing intracellular blockade of GABAA receptors by means of intracellular dialysis of a neuron with the pipette-filling solution, in which fluoride ions that hardly pass through the GABAA receptor channels substitute for Cl- and in which Mg2+ and ATP are omitted to induce rundown of the GABAA receptors during whole-cell patch-clamp recordings. However, the kinetics of suppression of GABAergic conductance and the effect on the currents mediated by glutamate receptors remain unknown. Here, using whole-cell recordings with fluoride-based, Mg2+- and ATP-free solution on CA3 hippocampal neurons of neonatal rats, we show that after 1 h of such dialysis, both spontaneous and evoked GABAA-receptor-mediated synaptic currents and responses induced by the GABAA receptor agonist isoguvacine were completely suppressed. Inward GABAergic postsynaptic currents were suppressed prior to outward currents. Synaptic responses mediated by AM PA receptors were not affected by the dialysis, whereas the NM DA-receptor-mediated postsynaptic currents were reduced by approximately 20%. Dialysis with fluoride-based Mg2+, ATP-free solution either fully blocked giant depolarizing potentials (G DPs) in CA3 pyramidal cells (n = 2) or reduced the charge crossing the membrane during G DPs and shifted the G DP reversal potential to more positive values (n = 5). The dialysis-resistant component of G DPs was mediated by glutamate receptors, since: (i) it reversed around 0 mV; (ii) it demonstrated a negative slope conductance at negative membrane voltages, which is characteristic of NM DA receptor-mediated responses; (iii) kinetics of the individual events composing the dialysis-resistant component of G DPs at negative voltages were very similar to those of AM PA receptor-mediated synaptic currents. Thus, this procedure can be useful to isolate the glutamate receptor-mediated component of neuronal network-driven activities

Intracellular blockade of GABAA receptors in the rat hippocampal neurons

The intracellular blockade of GABAA-receptor-mediated currents is a useful approach to suppress the GABAergic conductance in a single cell and to isolate the glutamatergic component of network-driven activities. Previously an approach has been described allowing intracellular blockade of GABA A receptors by means of intracellular dialysis of a neuron with the pipette-filling solution, in which fluoride ions that hardly pass through the GABAA receptor channels substitute for Cl- and in which Mg2+ and ATP are omitted to induce rundown of the GABAA receptors during whole-cell patch-clamp recordings. However, the kinetics of suppression of GABAergic conductance and the effect on the currents mediated by glutamate receptors remain unknown. Here, using whole-cell recordings with fluoride-based, Mg2+- and ATP-free solution on CA3 hippocampal neurons of neonatal rats, we show that after 1 h of such dialysis, both spontaneous and evoked GABAA-receptor-mediated synaptic currents and responses induced by the GABAA receptor agonist isoguvacine were completely suppressed. Inward GABAergic postsynaptic currents were suppressed prior to outward currents. Synaptic responses mediated by AMPA receptors were not affected by the dialysis, whereas the NMDA-receptor-mediated postsynaptic currents were reduced by approximately 20%. Dialysis with fluoride-based Mg 2+, ATP-free solution either fully blocked giant depolarizing potentials (GDPs) in CA3 pyramidal cells (n = 2) or reduced the charge crossing the membrane during GDPs and shifted the GDP reversal potential to more positive values (n = 5). The dialysis-resistant component of GDPs was mediated by glutamate receptors, since: (i) it reversed around 0 mV; (ii) it demonstrated a negative slope conductance at negative membrane voltages, which is characteristic of NMDA receptor-mediated responses; (iii) kinetics of the individual events composing the dialysis-resistant component of GDPs at negative voltages were very similar to those of AMPA receptor-mediated synaptic currents. Thus, this procedure can be useful to isolate the glutamate receptor-mediated component of neuronal network-driven activities. © 2014 Pleiades Publishing, Ltd

Dynamic changes from depolarizing to hyperpolarizing GABAergic actions during giant depolarizing potentials in the neonatal rat hippocampus

© 2015 the authors. During development, GABA exerts depolarizing action on immature neurons and, acting in synergy with glutamate, drives giant depolarizing potentials (GDPs) in the hippocampal network. Yet, blockade of the GABA(A) receptors transforms GDPs to epileptiform discharges suggesting dual, both excitatory and inhibitory, actions of GABA in the immature hippocampal network. However, the nature of this dualism in early GABA actions is poorly understood. Here we characterized the dynamics of synaptic currents mediated by GABA(A) and glutamate receptors through an estimation of the changes in their conductance and driving forces in neonatal rat CA3 pyramidal cells during GDPs. We found that depolarizing GABAergic and glutamatergic currents act in synergy at the GDPs’ onset. However, during the peak of the population discharge, the inward synaptic current was essentially mediated by glutamate receptors whereas GABA currents transiently switched their direction from depolarizing to hyperpolarizing as a result of neuronal depolarization above the GABA(A) reversal potential. Thus, the action of GABA on CA3 pyramidal cells dynamically changes during GDPs from excitatory at the GDPs’ onset to inhibitory at the GDPs’ peak. We propose that the dynamic changes in GABA actions occurring during GDPs enable GABAergic interneurons not only to initiate the discharge of pyramidal cells but also to control excitation in the recurrent CA3 network preventing epileptiform synchronization