152 research outputs found

    Atomic levels in superstrong magnetic fields and D=2 QED of massive electrons: screening

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    The photon polarization operator in superstrong magnetic fields induces the dynamical photon "mass" which leads to screening of Coulomb potential at small distances z1/mz\ll 1/m, mm is the mass of an electron. We demonstrate that this behaviour is qualitatively different from the case of D=2 QED, where the same formula for a polarization operator leads to screening at large distances as well. Because of screening the ground state energy of the hydrogen atom at the magnetic fields Bm2/e3B \gg m^2/e^3 has the finite value E0=me4/2ln2(1/e6)E_0 = -me^4/2 \ln^2(1/e^6).Comment: 12 pages, 2 figure

    Black-hole concept of a point-like nucleus with supercritical charge

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    The Dirac equation for an electron in the central Coulomb field of a point-like nucleus with the charge greater than 137 is considered. This singular problem, to which the fall-down onto the centre is inherent, is addressed using a new approach, based on a black-hole concept of the singular centre and capable of producing cut-off-free results. To this end the Dirac equation is presented as a generalized eigenvalue boundary problem of a self-adjoint operator. The eigenfunctions make complete sets, orthogonal with a singular measure, and describe particles, asymptotically free and delta-function-normalizable both at infinity and near the singular centre r=0r=0. The barrier transmission coefficient for these particles responsible for the effects of electron absorption and spontaneous electron-positron pair production is found analytically as a function of electron energy and charge of the nucleus. The singular threshold behaviour of the corresponding amplitudes substitutes for the resonance behaviour, typical of the conventional theory, which appeals to a finite-size nucleus.Comment: 22 pages, 5 figures, LATEX requires IOPAR

    Real and virtual photons in an external constant electromagnetic field of most general form

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    The photon behavior in an arbitrary superposition of constant magnetic and electric fields is considered on most general grounds basing on the first principles like Lorentz- gauge- charge- and parity-invariance. We make model- and approximation-independent, but still rather informative, statements about the behavior that the requirement of causal propagation prescribes to massive and massless branches of dispersion curves, and describe the way the eigenmodes are polarized. We find, as a consequence of Hermiticity in the transparency domain, that adding a smaller electric field to a strong magnetic field in parallel to the latter causes enhancement of birefringence. We find the magnetic field produced by a point electric charge far from it (a manifestation of magneto-electric phenomenon). We establish degeneracies of the polarization tensor that (under special kinematic conditions) occur due to space-time symmetries of the vacuum left after the external field is imposed.Comment: 30 pages, 1 figure, 57 equations, reference list of 38 item

    Modification of Coulomb law and energy levels of the hydrogen atom in a superstrong magnetic field

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    We obtain the following analytical formula which describes the dependence of the electric potential of a point-like charge on the distance away from it in the direction of an external magnetic field B: \Phi(z) = e/|z| [ 1- exp(-\sqrt{6m_e^2}|z|) + exp(-\sqrt{(2/\pi) e^3 B + 6m_e^2} |z|) ]. The deviation from Coulomb's law becomes essential for B > 3\pi B_{cr}/\alpha = 3 \pi m_e^2/e^3 \approx 6 10^{16} G. In such superstrong fields, electrons are ultra-relativistic except those which occupy the lowest Landau level (LLL) and which have the energy epsilon_0^2 = m_e^2 + p_z^2. The energy spectrum on which LLL splits in the presence of the atomic nucleus is found analytically. For B > 3 \pi B_{cr}/\alpha, it substantially differs from the one obtained without accounting for the modification of the atomic potential.Comment: version to be published in Physical Review D (incorrect "Keywords" in previous version have been cancelled

    Bethe-Salpeter approach for relativistic positronium in a strong magnetic field

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    We study the electron-positron system in a strong magnetic field using the differential Bethe-Salpeter equation in the ladder approximation. We derive the fully relativistic two-dimensional form that the four-dimensional Bethe-Salpeter equation takes in the limit of asymptotically strong constant and homogeneous magnetic field. An ultimate value for the magnetic field is determined, which provides the full compensation of the positronium rest mass by the binding energy in the maximum symmetry state and vanishing of the energy gap separating the electron-positron system from the vacuum. The compensation becomes possible owing to the falling to the center phenomenon that occurs in a strong magnetic field because of the dimensional reduction. The solution of the Bethe-Salpeter equation corresponding to the vanishing energy-momentum of the electron-positron system is obtained.Comment: 35 pages, minor correction

    Electric field of a pointlike charge in a strong magnetic field and ground state of a hydrogenlike atom

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    In an external constant magnetic field, so strong that the electron Larmour length is much shorter than its Compton length, we consider the modification of the Coulomb potential of a point charge owing to the vacuum polarization. We establish a short-range component of the static interaction in the Larmour scale, expressed as a Yukawa-like law, and reveal the corresponding "photon mass" parameter. The electrostatic force regains its long-range character in the Compton scale: the tail of the potential follows an anisotropic Coulomb law, decreasing away from the charge slower along the magnetic field and faster across. In the infinite-magnetic-field limit the potential is confined to an infinitely thin string passing though the charge parallel to the external field. This is the first evidence for dimensional reduction in the photon sector of quantum electrodynamics. The one-dimensional form of the potential on the string is derived that includes a delta-function centered in the charge. The nonrelativistic ground-state energy of a hydrogenlike atom is found with its use and shown not to be infinite in the infinite-field limit, contrary to what was commonly accepted before, when the vacuum polarization had been ignored. These results may be useful for studying properties of matter at the surface of extremely magnetized neutron stars.Comment: 45 pages, 6 figures, accepted to Phys. Rev.

    Polarization Evolution in Strong Magnetic Fields

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    Extremely strong magnetic fields change the vacuum index of refraction. Although this polarization dependent effect is small for typical neutron stars, it is large enough to decouple the polarization states of photons traveling within the field. The photon states evolve adiabatically and follow the changing magnetic field direction. The combination of a rotating magnetosphere and a frequency dependent state decoupling predicts polarization phase lags between different wave bands, if the emission process takes place well within the light cylinder. This QED effect may allow observations to distinguish between different pulsar emission mechanisms and to reconstruct the structure of the magnetosphere.Comment: 22 pages, 10 figures, accepted for publication in MNRA

    Testing of CP, CPT and causality violation with the light propagation in vacuum in presence of the uniform electric and magnetic fields

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    We have considered the structure of the fundamental symmetry violating part of the photon refractive index in vacuum in the presence of constant electric and magnetic fields. This part of the refractive index can, in principle, contain CPT symmetry breaking terms. Some of the terms violate Lorentz invariance, whereas the others violate locality and causality. Estimates of these effects, using laser experiments are considered.Comment: 12 page

    Self-adjoint extensions and spectral analysis in Calogero problem

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    In this paper, we present a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential αx2\alpha x^{-2}. Although the problem is quite old and well-studied, we believe that our consideration, based on a uniform approach to constructing a correct quantum-mechanical description for systems with singular potentials and/or boundaries, proposed in our previous works, adds some new points to its solution. To demonstrate that a consideration of the Calogero problem requires mathematical accuracy, we discuss some "paradoxes" inherent in the "naive" quantum-mechanical treatment. We study all possible self-adjoint operators (self-adjoint Hamiltonians) associated with a formal differential expression for the Calogero Hamiltonian. In addition, we discuss a spontaneous scale-symmetry breaking associated with self-adjoint extensions. A complete spectral analysis of all self-adjoint Hamiltonians is presented.Comment: 39 page
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