Magnetic monopoles have been a subject of study for more than a century since the first ideas by A. Vaschy and P. Curie, circa 1890. In 1974, Y. Nambu proposed a model for magnetic monopoles exploring a parallelism between the broken symmetry Higgs a
nd the superconductivity Ginzburg-Landau theories in order to describe the pions quark-antiquark confinement states. There, Nambu describes an energetic string where its end points behave like two magnetic monopoles with opposite magnetic charges -- quark and antiquark. Consequently, not only the interaction among monopole and antimonopole, mediated by a massive vector boson (Yukawa potential), but also the energetic string (linear potential) contributes to the effective interaction potential. We propose here a monopole-antimonopole non confining attractive interaction of the Nambu-type, and then investigate the formation of bound states, the monopolium. Some necessary conditions for the existence of bound states to be fulfilled by the proposed Nambu-type potential, Kato weakness, Set^o and Bargmann conditions, are verified. In the following, ground state energies are estimated for a variety of monopolium reduced mass, from $10^2$MeV to $10^2$TeV, and Compton interaction lengths, from $10^{-2}$am to $10^{-1}$pm, where discussion about non relativistic and relativistic limits validation is carried out.
Quantum parity conservation is verified at all orders in perturbation theory for a massless parity-even $U(1)times U(1)$ planar quantum electrodynamics (QED$_3$) model. The presence of two massless fermions requires the Lowenstein-Zimmermann (LZ) sub
traction scheme, in the framework of the Bogoliubov-Parasiuk-Hepp-Zimmermann-Lowenstein (BPHZL) renormalization method, in order to subtract the infrared divergences induced by the ultraviolet subtractions at 1- and 2-loops, however thanks to the superrenormalizability of the model the ultraviolet divergences are bounded up to 2-loops. Finally, it is proved that the BPHZL renormalization method preserves parity for the model taken into consideration, contrary to what happens to the ordinary massless parity-even $U(1)$ QED$_3$.
The Brown-Ravenhall operator was initially proposed as an alternative to describe the fermion-fermion interaction via Coulomb potential and subject to relativity. This operator is defined in terms of the associated Dirac operator and the projection o
nto the positive spectral subspace of the free Dirac operator. In this paper, we propose to analyze a modified version of the Brown-Ravenhall operator in two-dimensions. More specifically, we consider the Brown-Ravenhall operator with an attractive potential given by a Bessel-Macdonald function (also known as $K_0$-potential) using the Foldy-Wouthuysen unitary transformation. The $K_0$-potential is derived of the parity-preserving ${rm QED}_3$ model as a framework for evaluation of the fermion-fermion interaction potential. We prove that the two-dimensional Brown-Ravenhall operator with $K_0$-potential is bounded from below when the coupling constant is below a specified critical value (a property also referred to as stability). As by product, it is shown that the operator is in fact positive. We also investigate the location and nature of the spectrum of the Brown-Ravenhall operator with $K_0$-potential.
The parity-preserving $U(1)times U(1)$ massless QED$_3$ is proposed as a pristine graphene-like planar quantum electrodynamics model. The spectrum content, the degrees of freedom, spin, masses and charges of the quasiparticles (electron-polaron, hole
-polaron, photon and Neel quasiparticles) which emerge from the model are discussed. The four-fold broken degeneracy of the Landau levels, similar as the one experimentally observed in pristine graphene submitted to high applied external magnetic fields, is obtained. Furthermore, the model exhibits zero-energy Landau level indicating a kind of anomalous quantum Hall effect. The electron-polaron--electron-polaron scattering potentials in $s$- and $p$-wave states mediated by photon and Neel quasiparticles are computed and analyzed. Finally, the model foresees that two electron-polarons ($s$-wave state) belonging to inequivalent $mathbf{K}$ and $mathbf{K^prime}$ points in the Brillouin zone might exhibit attractive interaction, while two electron-polarons ($p$-wave state) lying both either in $mathbf{K}$ or in $mathbf{K^prime}$ points experience repulsive interaction.
The parity-preserving $U_A(1)times U_a(1)$ massive QED$_3$ is ultraviolet finiteness -- exhibits vanishing $beta$-functions, associated to the gauge coupling constants (electric and pseudochiral charges) and the Chern-Simons mass parameter, and all t
he anomalous dimensions of the fields -- as well as is parity and gauge anomaly free at all orders in perturbation theory. The proof is independent of any regularization scheme and it is based on the quantum action principle in combination with general theorems of perturbative quantum field theory by adopting the Becchi-Rouet-Stora (BRS) algebraic renormalization method in the framework of Bogoliubov-Parasiuk-Hepp-Zimmermann (BPHZ) subtraction scheme.
We analyze the Schrodinger operator in two-dimensions with an attractive potential given by a Bessel-Macdonald function. This operator is derived in the non-relativistic approximation of planar quantum electrodynamics (${rm QED}_3$) models as a frame
work for evaluation of two-quasiparticle scattering potentials. The analysis is motivated keeping in mind the fact that parity-preserving ${rm QED}_3$ models can provide a possible explanation for the behavior of superconductors. Initially, we study the self-adjointness and spectral properties of the Schrodinger operator modeling the non-relativistic approximation of these ${rm QED}_3$ models. Then, by using {em Set^o-type estimates}, an estimate is derived of the number of two-particle bound states which depends directly on the value of the effective coupling constant, $C$, for {em any} value of the angular momentum. In fact, this result in connection with the condition that guarantees the self-adjointness of the Schrodinger operator shows that there can always be a large number of two-quasiparticle bound states in planar quantum electrodynamics models. In particular, we show the existence of an isolated two-quasiparticle bound state if the effective coupling constant $C in (0,2)$ in case of zero angular momentum. To the best of our knowledge, this result has not yet been addressed in the literature. Additionally, we obtain an explicit estimate for the energy gap of two-quasiparticle bound states which might be applied to high-$T_c$ $s$-wave Cooper-type superconductors as well as to $s$-wave electron-polaron--electron-polaron bound states (bipolarons) in mass-gap graphene systems.
The Ostwald ripening phenomenon for gas bubbles in a liquid consists mainly in gas transfer from smaller bubbles to larger bubbles. An experiment was carried out in which the Ostwald ripening for air bubbles, in a liquid fluid with some rheological p
arameters of the human blood, is reproduced. There it has been measured time evolution of bubbles mean radius, number of bubbles and radius size distribution, where the initial bubbles radii normalized distribution behaves like a Tsallis ($q$-Weibull) distribution. One of the main results shows that, while the number of bubbles decreases in time the bubbles mean radius increases, therefore smaller bubbles disappear whereas the, potentially dangerous for the diver, larger bubbles grow up. Consequently, it is presumed that such a bubble broadening effect could contribute, even minimally, to decompression illness: decompression sickness and arterial gas embolism. This conjecture is reinforced by the preliminary results of Ostwald broadening to RGBM (Reduced Gradient Bubble Model) decompression schedules for a closed circuit rebreather (CCR) dive to 420fsw (128m) with 21/79 Heliox gas mixture.
The measure of quantum entanglement is determined for any dimer, either ferromagnetic or antiferromagnetic, spin-1/2 Heisenberg systems in the presence of external magnetic field. The physical quantity proposed as a measure of thermal quantum entangl
ement is the distance between states defined through the Hilbert-Schmidt norm. It has been shown that for ferromagnetic systems there is no entanglement at all. However, although under applied magnetic field, antiferromagnetic spin-1/2 dimers exhibit entanglement for temperatures below the decoherence temperature -- the one above which the entanglement vanishes. In addition to that, the decoherence temperature shows to be proportional to the exchange coupling constant and independent on the applied magnetic field, consequently, the entanglement may not be destroyed by external magnetic fields -- the phenomenon of {it magnetic shielding effect of quantum entanglement states}. This effect is discussed for the binuclear nitrosyl iron complex [Fe$_2$(SC$_3$H$_5$N$_2$)$_2$(NO)$_4$] and it is foreseen that the quantum entanglement survives even under high magnetic fields of Tesla orders of magnitude.
The issue intensively claimed in the literature on the generation of a CPT-odd and Lorentz violating Chern-Simons-like term by radiative corrections owing to a CPT violating interaction -- the axial coupling of fermions with a constant vector field $
b_m$ -- is mistaken. The presence of massless gauge field triggers IR divergences that might show up from the UV subtractions, therefore, so as to deal with the (actual physical) IR divergences, the Lowenstein-Zimmermann subtraction scheme, in the framework of BPHZL renormalization method, has to be adopted. The proof on the non generation of such a Chern-Simons-like term is done, independent of any kind of regularization scheme, at all orders in perturbation theory.
A Lorentz invariant version of a mass-gap graphene-like planar quantum electrodynamics, the parity-preserving $U(1)times U(1)$ massive QED$_3$, exhibits attractive interaction in low-energy electron-polaron--electron-polaron $s$-wave scattering, favo
ring quasiparticles bound states, the $s$-wave bipolarons.
