152 research outputs found
Atomic levels in superstrong magnetic fields and D=2 QED of massive electrons: screening
The photon polarization operator in superstrong magnetic fields induces the
dynamical photon "mass" which leads to screening of Coulomb potential at small
distances , 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 has the finite value .Comment: 12 pages, 2 figure
Black-hole concept of a point-like nucleus with supercritical charge
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
. 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
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
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
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
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
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
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
In this paper, we present a mathematically rigorous quantum-mechanical
treatment of a one-dimensional motion of a particle in the Calogero potential
. 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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