231 research outputs found

### Gravitational Correction to Vacuum Polarization

We consider the gravitational correction to (electronic) vacuum polarization
in the presence of a gravitational background field. The Dirac propagators for
the virtual fermions are modified to include the leading gravitational
correction (potential term) which corresponds to a coordinate-dependent fermion
mass. The mass term is assumed to be uniform over a length scale commensurate
with the virtual electron-positron pair. The on-mass shell renormalization
condition ensures that the gravitational correction vanishes on the mass shell
of the photon, i.e., the speed of light is unaffected by the quantum field
theoretical loop correction, in full agreement with the equivalence principle.
Nontrivial corrections are obtained for off-shell, virtual photons. We compare
our findings to other works on generalized Lorentz transformations and combined
quantum-electrodynamic gravitational corrections to the speed of light which
have recently appeared in the literature.Comment: 9 pages; RevTeX; typographical errors corrected and references adde

### Light Sea Fermions in Electron-Proton and Muon-Proton Interactions

The proton radius conundrum [R. Pohl et al., Nature vol.466, p.213 (2010) and
A. Antognini et al., Science vol.339, p.417 (2013)] highlights the need to
revisit any conceivable sources of electron-muon nonuniversality in
lepton-proton interactions within the Standard Model. Superficially, a number
of perturbative processes could appear to lead to such a nonunversality. One of
these is a coupling of the scattered electron into an electronic as opposed to
a muonic vacuum polarization loop in the photon exchange of two valence quarks,
which is present only for electron projectiles as opposed to muon projectiles.
However, we can show that this effect actually is part of the radiative
correction to the proton's polarizability contribution to the Lamb shift,
equivalent to a radiative correction to double scattering. We conclude that any
conceivable genuine nonuniversality must be connected with a nonperturbative
feature of the proton's structure, e.g., with the possible presence of light
sea fermions as constituent components of the proton. If we assume an average
of roughly 0.7*10^(-7) light sea positrons per valence quark, then we can show
that virtual electron-positron annihiliation processes lead to an extra term in
the electron-proton versus muon-proton interaction, which has the right sign
and magnitude to explain the proton radius discrepancy.Comment: 6 pages; RevTeX; published in Physical Review A in 2013; as compare
to the journal version, we have added a note at the end of the paper which
pertains to the (new) Ref. [42]; otherwise unchange

### A Problematic Set of Two-Loop Self-Energy Corrections

We investigate a specific set of two-loop self-energy corrections involving
squared decay rates and point out that their interpretation is highly
problematic. The corrections cannot be interpreted as radiative energy shifts
in the usual sense. Some of the problematic corrections find a natural
interpretation as radiative nonresonant corrections to the natural line shape.
They cannot uniquely be associated with one and only one atomic level. While
the problematic corrections are rather tiny when expressed in units of
frequency (a few Hertz for hydrogenic P levels) and do not affect the
reliability of quantum electrodynamics at the current level of experimental
accuracy, they may be of importance for future experiments. The problems are
connected with the limitations of the so-called asymptotic-state approximation
which means that atomic in- and out-states in the S-matrix are assumed to have
an infinite lifetime.Comment: 12 pages, 3 figures (New J. Phys., in press, submitted 28th May

### Separation of Transitions with Two Quantum Jumps from Cascades

We consider the general scenario of an excited level |i> of a quantum system
that can decay via two channels: (i) via a single-quantum jump to an
intermediate, resonant level |bar m>, followed by a second single-quantum jump
to a final level |f>, and (ii) via a two-quantum transition to a final level
|f>. Cascade processes |i> -> |bar m> -> | f> and two-quantum transitions |i>
-> |m> -> |f> compete (in the latter case, |m> can be both a nonresonant as
well as a resonant level). General expressions are derived within second-order
time-dependent perturbation theory, and the cascade contribution is identified.
When the one-quantum decay rates of the virtual states are included into the
complex resonance energies that enter the propagator denominator, it is found
that the second-order decay rate contains the one-quantum decay rate of the
initial state as a lower-order term. For atomic transitions, this implies that
the differential-in-energy two-photon transition rate with complex resonance
energies in the propagator denominators can be used to good accuracy even in
the vicinity of resonance poles.Comment: 9 pages; RevTe

### Dirac Hamiltonian with Imaginary Mass and Induced Helicity-Dependence by Indefinite Metric

It is of general theoretical interest to investigate the properties of
superluminal matter wave equations for spin one-half particles. One can either
enforce superluminal propagation by an explicit substitution of the real mass
term for an imaginary mass, or one can use a matrix representation of the
imaginary unit that multiplies the mass term. The latter leads to the tachyonic
Dirac equation, while the equation obtained by the substitution m->i*m in the
Dirac equation is naturally referred to as the imaginary-mass Dirac equation.
Both the tachyonic as well as the imaginary-mass Dirac Hamiltonians commute
with the helicity operator. Both Hamiltonians are pseudo-Hermitian and also
possess additional modified pseudo-Hermitian properties, leading to constraints
on the resonance eigenvalues. Here, by an explicit calculation, we show that
specific sum rules over the spectrum hold for the wave functions corresponding
to the well-defined real energy eigenvalues and complex resonance and
anti-resonance energies. In the quantized imaginary-mass Dirac field,
one-particle states of right-handed helicity acquire a negative norm
("indefinite metric") and can be excluded from the physical spectrum by a
Gupta--Bleuler type condition.Comment: 8 pages; RevTeX; published in J.Mod.Phy

### Muonic bound systems, virtual particles and proton radius

The proton radius puzzle questions the self-consistency of theory and
experiment in light muonic and electronic bound systems. Here, we summarize the
current status of virtual particle models as well as Lorentz-violating models
that have been proposed in order to explain the discrepancy. Highly charged
one-electron ions and muonic bound systems have been used as probes of the
strongest electromagnetic fields achievable in the laboratory. The average
electric field seen by a muon orbiting a proton is comparable to hydrogenlike
Uranium and, notably, larger than the electric field in the most advanced
strong-laser facilities. Effective interactions due to virtual annihilation
inside the proton (lepton pairs) and process-dependent corrections (nonresonant
effects) are discussed as possible explanations of the proton size puzzle. The
need for more experimental data on related transitions is emphasized.Comment: 11 pages; RevTe

### Long-Range Atom-Wall Interactions and Mixing Terms: Metastable Hydrogen

We investigate the interaction of metastable 2S hydrogen atoms with a
perfectly conducting wall, including parity-breaking S-P mixing terms (with
full account of retardation). The neighboring 2P_1/2 and 2P_3/2 levels are
found to have a profound effect on the transition from the short-range,
nonrelativistic regime, to the retarded form of the Casimir-Polder interaction.
The corresponding P state admixtures to the metastable 2S state are calculated.
We find the long-range asymptotics of the retarded Casimir-Polder potentials
and mixing amplitudes, for general excited states, including a fully quantum
electrodynamic treatment of the dipole-quadrupole mixing term. The decay width
of the metastable 2S state is roughly doubled even at a comparatively large
distance of 918 atomic units (Bohr radii) from the perfect conductor. The
magnitude of the calculated effects is compared to the unexplained Sokolov
effect.Comment: 6 pages; RevTe

### Techniques in Analytic Lamb Shift Calculations

Quantum electrodynamics has been the first theory to emerge from the ideas of
regularization and renormalization, and the coupling of the fermions to the
virtual excitations of the electromagnetic field. Today, bound-state quantum
electrodynamics provides us with accurate theoretical predictions for the
transition energies relevant to simple atomic systems, and steady theoretical
progress relies on advances in calculational techniques, as well as numerical
algorithms. In this brief review, we discuss one particular aspect connected
with the recent progress: the evaluation of relativistic corrections to the
one-loop bound-state self-energy in a hydrogenlike ion of low nuclear charge
number, for excited non-S states, up to the order of alpha (Zalpha)^6 in units
of the electron mass. A few details of calculations formerly reported in the
literature are discussed, and results for 6F, 7F, 6G and 7G states are given.Comment: 16 pages, LaTe

### Fine-Structure Constant for Gravitational and Scalar Interactions

Starting from the coupling of a relativistic quantum particle to the curved
Schwarzschild space-time, we show that the Dirac--Schwarzschild problem has
bound states and calculate their energies including relativistic corrections.
Relativistic effects are shown to be suppressed by the gravitational
fine-structure constant alpha_G = G m_1 m_2/(hbar c), where G is Newton's
gravitational constant, c is the speed of light and m_1 and m_2 >> m_1 are the
masses of the two particles. The kinetic corrections due to space-time
curvature are shown to lift the familiar (n,j) degeneracy of the energy levels
of the hydrogen atom. We supplement the discussion by a consideration of an
attractive scalar potential, which, in the fully relativistic Dirac formalism,
modifies the mass of the particle according to the replacement m -> m (1 -
\lambda/r), where r is the radial coordinate. We conclude with a few comments
regarding the (n,j) degeneracy of the energy levels, where n is the principal
quantum number, and j is the total angular momentum, and illustrate the
calculations by way of a numerical example.Comment: 6 pages; RevTe

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