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We study the coupling of N charged scalar particles plus the electromagnetic field to Arnowitt–Deser–Misner (ADM) tetrad gravity and its canonical formulation in asymptotically Minkowskian space–times without super-translations. To regularize the self-energies, both the electric charge and the sign of the energy of the particles are Grassmann-valued. The introduction of the noncovariant radiation gauge allows reformulation of the theory in terms of transverse electromagnetic fields and to extract the generalization of the Coulomb interaction among the particles in the riemannian instantaneous 3-spaces of global noninertial frames, the only ones allowed by the equivalence principle. Then we make the canonical transformation to the York canonical basis, where there is a separation between the inertial (gauge) variables and the tidal ones inside the gravitational field and a special role of the eulerian observers associated with the 3+1 splitting of space–time. The Dirac hamiltonian is weakly equal to the weak ADM energy. The Hamilton equations in Schwinger time gauges are given explicitly. In the York basis they are naturally divided into four sets: (i) the contracted Bianchi identities; (ii) the equations for the inertial gauge variables; (iii) the equations for the tidal ones; and (iv) the equations for matter. Finally, we give the restriction of the Hamilton equations and of the constraints to the family of nonharmonic 3-orthogonal gauges, in which the instantaneous riemannian 3-spaces have a nonfixed trace 3K of the extrinsic curvature but a diagonal 3-metric. The inertial gauge variable 3K (the general-relativistic remnant of the freedom in the clock synchronization convention) gives rise to a negative kinetic term in the weak ADM energy vanishing only in the gauges with 3K = 0: is it relevant for dark energy and back-reaction? In the second paper will appear the linearization of the theory in these nonharmonic 3-orthogonal gauges to obtain hamiltonian post-minkowskian gravity (without post-newtonian approximations) with asymptotic Minkowski background, nonflat instantaneous 3-spaces and no post-newtonian expansion. This will allow the exploration of the inertial effects induced by the York time 3K in nonflat 3-spaces (they do not exist in newtonian gravity) and to check how well dark matter can be explained as an inertial aspect of Einstein’s general relativity: this will be done in a third paper on the post-minkowskian 2-body problem in the absence of the electromagnetic field and on its 0.5 post-newtonian limit.

In this second paper we define a post-minkowskian (PM) weak field approximation leading to a linearization of the Hamilton equations of Arnowitt–Deser–Misner (ADM) tetrad gravity in the York canonical basis in a family of nonharmonic 3-orthogonal Schwinger time gauges. The York time 3K (the relativistic inertial gauge variable, not existing in newtonian gravity, parametrizing the family, and connected to the freedom in clock synchronization, i.e., to the definition of the the shape of the instantaneous 3-spaces) is set equal to an arbitrary numerical function. The matter are considered point particles, with a Grassmann regularization of self-energies, and the electromagnetic field in the radiation gauge: an ultraviolet cutoff allows a consistent linearization, which is shown to be the lowest order of a hamiltonian PM expansion. We solve the constraints and the Hamilton equations for the tidal variables and we find PM gravitational waves with asymptotic background (and the correct quadrupole emission formula) propagating on dynamically determined non-euclidean 3-spaces. The conserved ADM energy and the Grassmann regularization of self-energies imply the correct energy balance. A generalized transverse–traceless gauge can be identified and the main tools for the detection of gravitational waves are reproduced in these nonharmonic gauges. In conclusion, we get a PM solution for the gravitational field and we identify a class of PM Einstein space–times, which will be studied in more detail in a third paper together with the PM equations of motion for the particles and their post-newtonian expansion (but in the absence of the electromagnetic field). Finally we make a discussion on the gauge problem in general relativity to understand which type of experimental observations may lead to a preferred choice for the inertial gauge variable 3K in PM space–times. In the third paper we will show that this choice is connected with the problem of dark matter.

The rotational spectrum of methanol in its third excited torsional state, vt = 3, as well as the K = 0 A-state of vt = 4, has been recorded and analyzed in the 8–1654 GHz frequency range. The vt = 3 state lies well above the top of the torsional barrier and the majority of the energy origins for the various K sub-bands lie below the C-O stretching fundamental vibration. Only the a-type R-branch spectrum was observed in this frequency range, suggesting that the near torsional degeneracy required for a b-type spectrum in the microwave accidentally reduces the torsional overlap, making these transitions very weak. The A-state K = 4 of vt = 3 interaction with the C-O stretch torsional ground state K = 0+ and K = 1+ has been accounted for. The E-state K = –5 level could be fit directly with a power series in spite of its resonance with the C-O stretch torsional ground state K = –5 level. The aR-branch of the K = 0 A-state vt = 4 sub-band is also provided and the origin of this band resonance with the C-O stretch is discussed. The data have been modeled with a power series to near experimental accuracy. The measured and calculated spectrum should facilitate radio astronomical assignments of vt = 3 transitions in hot sources.

Accurate theoretical knowledge of the (1s2p)3P1–(1s2s)1S0 splitting in He-like ions is demanded for future experimental studies of the nuclear spin-dependent part of the weak interaction. In this paper we perform a calculation of the hyperfine structure of (1s2p)3P1–(1s2s)1S0 within 3 ≤ Z ≤ 35, Z being the atomic number. In this Z range parity nonconservation (PNC) effects are amplified by the close energy proximity of the opposite parity levels (1s2p)3P1 and (1s2s)1S0. We find that the hyperfine structure is relevant for Z > 12, and produces splitting among the hyperfine sublevels as large as 150 meV for medium Z He-like ions (Z ∼ 35).

In this paper, a new experiment is presented to measure the 1S–2S transition of positronium, the bound state of an electron and a positron. The goal is to improve the current accuracy by a factor of 5 to reach a precision of the order of 0.6 ppb, to check recent QED calculations. This accuracy is challenging, but it seems well within reach in view of the technological advances that have occurred during the last two decades. We will present the details of the experimental set-up, the advances in the production of positronium, the developments of the laser system, and as well our new experimental technique for the detection of Ps in the 2S state.

This paper reports on the current development of a new Thompson–Lampard calculable capacitor at LNE. The goal is to determine the von Klitzing constant RK at a significant level of uncertainty of about one part in 108. The comparison with other accurate measurements of h/e2 serves as a relevant test of validity of the theory predicting RK = h/e2, a decisive issue within the context of the new SI. Conversely, assuming that this relation is exact, the measurement of RK and thus that of the fine structure constant α can be used for testing quantum electrodynamics theory. The mechanical structure of the new LNE calculable cross capacitor has been designed and a new set of electrodes has been fabricated. The assembling of the calculable capacitor is in progress.

The pure vibrational transition frequencies of magnetically trapped cold XH molecules are useful to detect the variance in the proton-to-electron mass ratio β (X: alkali-earth atom). This paper compares the accuracies of the vibrational transition frequencies for different XH molecules.

Multi-level gaseous atomic systems showing electromagnetically induced transparency (EIT) phenomenon also exhibit low light intensity nonlinear optical phenomena. This is primarily due to the supression of linear susceptibility for the probe light during EIT. Therefore under EIT, nonlinear interactions become appreciable even at very low light intensities. In particular, Kerr nonlinearity in N systems irradiated by three fields has been both experimentally and theoretically investigated. In this paper, we report an all optical observation of an absorptive three-photon resonance feature, of subnatural width, in a N level scheme of gaseous rubidium, at room temperature, in a novel geometry of three independent beams. The non-Doppler free configuration of the beam in which the absorption is seen is the first such feature reported in a beam that is not directly taking part in the transparency effect. We have demonstrated the velocity selective nature of this absorption and studied the contrast dependence on detuning from the fourth level. Density matrix calculations have been carried out for this geometry, the results of which are in qualitative agreement with the experiment.

In this paper, we report on our recent advances on a new trap loading mechanism for neutral atoms. The idea is based on our recently published results for chromium spectroscopy of atoms released from a solid neon matrix at cryogenic temperatures. The proposed trap loading mechanism consists of magnetically capturing the low-energy fraction of paramagnetic atoms being released from the matrix, while the host Ne atoms stick to the walls. Two different designs are described: one with a superconducting magnet producing a trap depth of 3 T and another with a superconducting dynamically switched magnet that generates a trap depth of about 1 T. Some preliminary results are presented.

This paper presents a brief overview on the issue of singularity resolution in loop quantum gravity presented at the Theory Canada IV conference at the Centre de Recherches Math\'{e}matiques at the Universit\'{e} de Montr\'{e}al (June 4-7, 2008). The intended audience is theoretical physicists who are non-specialist in the field and therefore much of the technical detail is omitted here. Instead, a brief review of loop quantum gravity is presented, followed by a survey of previous and current work on results concerning the resolution of the classical black hole singularity within loop quantum gravity.

In this paper we derive an effective master equation and quantum trajectory equation for multiple qubits in a single resonator and in the large resonator decay limit. We show that homodyne measurement of the resonator transmission is a weak measurement of the collective qubit inversion. As an example of this result, we focus on the case of two qubits and show how this measurement can be used to generate an entangled state from an initially separable state. This is realized without relying on an entangling Hamiltonian. We show that, for current experimental values of both the decoherence and measurement rates, this approach can be used to generate highly entangled states. This scheme takes advantage of the fact that one of the Bell states is decoherence-free under Purcell decay.

CXO CDFS J033260.0-274748 is a quasi-stellar object (QSO) and identification of several emission lines observed in its optical spectrum has led to the determination of its redshift as 2.579. On the other hand, the Chandra ACIS-I spectrum has detected a strong absorption feature at the observed wavelength around 6.3 keV that cannot be identified under normal physical conditions. The authors have invoked an unusually large outflow bulk velocity of 0.7c–0.8c to explain the feature. However, such extraordinarily high bulk velocities are unprecedented in the extragalactic literature. We show here that the optical emission lines and the X-ray absorption feature can be identified with search lines of longer wavelengths that have been blueshifted and do not need any unusual physical conditions to be invoked. The blueshifted spectra are explained as being due to the net motion of the QSO along with the absorbing cloud towards the observer. Two scenarios are proposed, namely, the ejection mechanism and the multiverse.

The long quest for a measurement of the Lamb shift in muonic hydrogen is over. Last year we measured the 2S 1/2F=1 –2P 3/2F=2 energy splitting (Pohl et al., Nature, 466, 213 (2010)) in μp with an experimental accuracy of 15 ppm, twice better than our proposed goal. Using current QED calculations of the fine, hyperfine, QED, and finite size contributions, we obtain a root-mean-square proton charge radius of rp = 0.841 84 (67) fm. This value is 10 times more precise, but 5 standard deviations smaller, than the 2006 CODATA value of rp. The origin of this discrepancy is not known. Our measurement, together with precise measurements of the 1S–2S transition in regular hydrogen and deuterium, gives improved values of the Rydberg constant, R∞ = 10 973 731.568 160 (16) m–1 and the rms charge radius of the deuteron rd = 2.128 09 (31) fm.

We plan to measure several 2S–2P transition frequencies in μ4He+ and μ3He+ by means of laser spectroscopy with an accuracy of 50 ppm. This will lead to a determination of the corresponding nuclear rms charge radii with a relative accuracy of 3 × 10−4, limited by the uncertainty of the nuclear polarization contribution. First, these measurements will help to solve the proton radius puzzle. Second, these very precise nuclear radii are benchmarks for ab initio few-nucleon theories and potentials. Finally when combined with an ongoing measurement of the 1S–2S transition in He+, these measurements will lead to an enhanced bound-state QED test of the 1S Lamb shift in He+.

In this contribution to PSAS 2010, we report on recent progress on an experiment aimed at measuring small optical directional anisotropies by frequency metrology in a high-finesse ring cavity. We focus on our first experimental goal, the measurement of magneto-electric effects in gases. After a review of the expected effects in our set-up, we present the apparatus and the measurement procedure, showing that we already have the necessary sensitivity to start novel experiments.

We extend the results of Bakalov et al. (Phys. Rev. Lett. 84, 2350 (2000)) on one-photon electric dipole transition line shift and broadening to the case of two-photon transitions. As an example, we consider the laser-induced transition in antiprotonic helium produced in a helium gas target. The transition is between antiprotonic helium states (n, l) = (33, 32) and (31, 30).

The method of two-photon approximation for multiphoton decay is applied to the decay of the 4d state in the hydrogen atom. In the process of four-photon decay the two-photon contribution that leads to radiation escape, from the interaction with matter, is considered. This may be helpful for a strict description of the recombination process in the hydrogen atom and, in principle, for the history of hydrogen recombination in the early universe.

We discuss the leading relativistic (nonrecoil and recoil) corrections to bound state g-factors of particles with arbitrary spin. These corrections are universal for any spin and depend only on the free particle gyromagnetic ratios. We explain the physical reasons behind this universality.

Atomic parity violation (APV) experiments are sensitive probes of the electroweak interaction at low energy. These experiments are competitive with and complementary to high-energy collider experiments. The APV signal is strongly enhanced in heavy atoms, and it is measurable by exciting suppressed (M1, E2) transitions. The predicted enhancement factor of the APV effect in the S-D transition in Ra+ is about 50 times larger than the S-S transition in neutral Cs. However, certain spectroscopic information on Ra+, needed to constrain the required atomic many-body theory, was lacking. Using the AGOR cyclotron and the TRIμP facility at KVI in Groningen, short-lived 212–214Ra+ ions were produced and trapped. First ever excited-state laser spectroscopy was performed on the trapped ions. These measurements provide a benchmark for the atomic theory required to extract the electroweak mixing angle to sub 1% accuracy and are an important step towards an APV experiment in a single trapped Ra+ ion. A lower bound on the radiative lifetime of the 62D5/2 state was found of 232(4) ms. This experimental confirmation of the long coherence time of the meta-stable 62D5/2 state is important in light of the possibility of using a single trapped radium ion as an optical frequency standard.

Precise spectroscopic experiments with light atoms can provide information about nuclear properties that are very difficult to obtain in electron scattering experiments. For example, relative nuclear radii of low-Z isotopes can be determined accurately from isotope shifts. Theory has attained sufficient accuracy to study exotic, short-lived halo nuclei by interpreting precise spectroscopic measurements. However, serious inconsistencies remain in the measured isotope shifts for the D1 and D2 lines of the stable isotopes (6Li and 7Li). The latest experiments, within the last decade, are in strong disagreement with each other and with theory. We report on the progress of a new experiment at the National Institute of Standards and Technology (NIST) to measure these lithium D lines using an optical frequency comb. A preliminary result for the splitting isotope shift (SIS) is presented.

Precise determination of bound-electron g-factors in highly charged ions provides stringent tests for state of the art theoretical calculations. The scope reaches from relativistic electron-correlation effects on the one hand to bound-state QED terms on the other. Besides, the investigation can contribute to the determination of the fine-structure constant α. In a first approach with boron-like ions of spinless nuclei (e.g., 40Ar13+ and 40Ca15+), we will excite the 22P1/2 – 22P3/2 fine-structure transition with laser radiation and probe microwave transitions between Zeeman sublevels. From this laser-microwave double-resonance technique the g-factor can be determined on a ppb level of accuracy. We have prepared a cryogenic trap assembly with a creation trap and a spectroscopy trap — a half-open compensated cylindrical Penning trap. Argon gas will be injected through a remotely controlled valve, working at cryogenic temperature and in the field of a superconducting magnet. Ions are produced by electron impact ionization and transferred to the spectroscopy trap. In the future, the trap will be connected to the HITRAP facility at GSI, and the method will be applied to hyperfine-structure transitions of hydrogen-like heavy ions to measure electronic and nuclear magnetic moments. We present important techniques employed in the experiment.

Calculational results are presented for the fine structure splitting of the 23P state of helium and helium-like ions with nuclear charge Z up to 10. Theoretical predictions are in agreement with the latest experimental results for the helium fine structure intervals as well as with the most of the experimental data available for light helium-like ions. Comparing the theoretical value of the 23P0-23P1 interval in helium with experimental results (Zelevinsky et al. Phys. Rev. Lett. 95, 203001 (2005)), we determine the value of the fine structure constant α with an accuracy of 31 ppb.

High resolution ro-vibrational spectroscopy of H 2+ or HD+ can lead to a significantly improved determination of the electron to proton mass ratio me/mp if the theoretical determination of transition frequencies becomes sufficiently accurate. We report on recent theoretical progress in the description of the hyperfine structure of H 2+ , as well as first steps in the evaluation of radiative corrections at order mα7. Completion of the latter calculation should allow us to reach the projected 10−10 accuracy level and open the road to mass ratio determination.

AEgIS (Antimatter experiment: gravity, interferometry, spectroscopy) is an experiment approved by CERN with the goal of studying antihydrogen physics. In AEgIS, antihydrogen will be produced by charge exchange reactions of cold antiprotons with positronium atoms excited in a Rydberg state (n > 20). In the first phase of the experiment, controlled acceleration by an electric field gradient (Stark effect) and subsequent measurement of free fall in a Moiré deflectometer will allow a test of the weak equivalence principle. In a second phase, the antihydrogen will be slowed, confined, and laser-cooled to perform CPT studies and detailed spectroscopy. In the present work, after a general description of the experiment, the present status of advancement will be reviewed, with special attention to the production and excitation of positronium atoms.

Antihydrogen spectroscopy promises precise tests of the symmetry of matter and antimatter, and can possibly offer new insights into the baryon asymmetry of the universe. Antihydrogen is, however, difficult to synthesize and is produced only in small quantities. The ALPHA collaboration is therefore pursuing a path towards trapping cold antihydrogen to permit the use of precision atomic physics tools to carry out comparisons of antihydrogen and hydrogen. ALPHA has addressed these challenges. Control of the plasma sizes has helped to lower the influence of the multipole field used in the neutral atom trap, and thus lowered the temperature of the created atoms. Finally, the first systematic attempt to identify trapped antihydrogen in our system is discussed. This discussion includes special techniques for fast release of the trapped anti-atoms, as well as a silicon vertex detector to identify antiproton annihilations. The silicon detector reduces the background of annihilations, including background from antiprotons that can be mirror trapped in the fields of the neutral atom trap. A description of how to differentiate between these events and those resulting from trapped antihydrogen atoms is also included.

The purpose of this article is twofold. First, we attempt to give a brief overview of the different application areas of quantum electrodynamics (QED). These include fundamental physics (prediction of atomic energy levels), where the atom may be exposed to additional external fields (hyperfine splitting and g factor). We also mention QED processes in highly intense laser fields and more applied areas like Casimir and Casimir–Polder interactions. Both the unifying aspects as well as the differences in the the theoretical treatment required by these application areas (such as the treatment of infinities) are highlighted. Second, we discuss an application of the formalism in the fundamentally interesting area of the prediction of energy levels, namely, the hyperfine structure of P states of muonic hydrogen.

Cooling antihydrogen atoms is important for future experiments both to test the fundamental CPT symmetry by high resolution laser spectroscopy and also to measure the gravitational acceleration of antimatter. Laser cooling of antihydrogen can be done on the strong 1S–2P transition at the wavelength of Lyman-alpha (121.6 nm). A continuous wave laser at the Lyman-alpha wavelength based on solid-state fundamental lasers is described. By using a two-photon and a near one-photon resonance a scan across the whole phase matching curve of the four-wave mixing process is possible. Furthermore the influence of the beam profile of one fundamental beam on the four-wave mixing process is studied.

We present preparatory measurements for an improved test of time dilation at the experimental storage ring (ESR) at GSI in Darmstadt. A unique combination of particle accelerator experiments and laser spectroscopy is used to perform this test with the highest precision. 7Li+ ions are accelerated to 34% of the speed of light at the GSI Helmholtzzentrum für Schwerionenforschung and stored in the experimental storage ring. The forward and backward Doppler shifts of an electric dipole transition of these ions are measured with laser spectroscopy techniques. From these Doppler shifts, both the ion velocity β = ν/c and the time dilation factor [Formula: see text] can be derived for testing Special Relativity. Two laser systems have been developed to drive the 3S1→3P2 transition in 7Li+. Moreover, a detector system composed of photomultipliers, both to monitor the exact laser ion beam overlap as well as to optimize fluorescence detection, has been set up and tested. We investigate optical-optical double-resonance spectroscopy on a closed Λ-type three-level system to overcome Doppler broadening. A residual, broadened fluorescence background caused by velocity-changing processes in the ion beam is identified, and a background subtraction scheme implemented. At the present stage the experimental sensitivity, although already comparable with previous measurements on slower ion beams at the TSR storage ring that led to [Formula: see text] –8, suffer from a poor signal-to-noise ratio. Modifications of the ion source as well as the detection system are discussed that promise to improve the sensitivity by one order of magnitude.

Atomic parity violation (APV) can be measured in a single Ra+ ion, enabling a precise measurement of the electroweak mixing angle in the Standard Model of particle physics at low momentum transfer. This provides sensitivity to new particles such as extra Z0 bosons or leptoquarks. The Weinberg angle can be measured via a determination of the light shift in the forbidden 72S1/2–62D3/2 transition in a single trapped Ra+. Ultra-narrow transitions in such an ideal system can also be exploited to realize a high stability frequency standard. At the TRIμP facility of KVI, we have succeeded in the production of a series of radioactive short-lived radium isotopes. The radium isotopes produced were stopped and thermalized to Ra+ in a thermal ionizer, mass separated in a Wien filter, cooled in a gas filled radio frequency quadrupole and subsequently trapped as a cloud in a linear Paul trap. Laser spectroscopy in the trapped radium ions has been performed. The results of hyperfine structure, isotope shift, and lifetime measurements are important experimental inputs to test the accuracy of atomic theory, the precision of which is indispensable for extracting the Weinberg angle. These results are also of relevance for a possible atomic clock, based on trapped Ra+.

The DAMA/LIBRA experiment has a sensitive mass of about 250 kg highly radiopure NaI(Tl). It is running at the Gran Sasso National Laboratory of the INFN in Italy and is mainly devoted to the investigation of dark matter (DM) particles in the galactic halo by exploiting the model-independent DM annual modulation signature. The present DAMA/LIBRA and the former DAMA/NaI experiments (the first generation experiment having an exposed mass of about 100 kg) have thus far cumulatively released the results of data collected over 13 annual cycles (total exposure: 1.17 t year). They give model-independent evidence of the presence of DM particles in the galactic halo on the basis of the investigated DM signature at 8.9 σ C.L. for the cumulative exposure. The main aspects of the obtained results are summarized and some comments are addressed.

The relativistic corrections to the theoretical oscillator strengths of light elements such as helium are typically less than 0.1% and usually are ignored. However, they can be important for comparisons with the most accurate experiments, and they rapidly increase in magnitude with increasing nuclear charge. We have begun with the spin-forbidden electric-dipole transitions of neutral helium, using calculations consisting of (1) extremely accurate wave functions without relativistic corrections for both infinite and finite nuclear mass, (2) spin-changing matrix elements through the perturbations of the wave functions by the spin-orbit and spin-other-orbit Breit operators, (3) the use of pseudostates in the sums over all the intermediate states including the continuum, and (4) the inclusion as perturbers of the 1S0 and 3S1 states the pseudostates corresponding to the doubly excited npn′p 3P 0e and npn′p 1P 1e terms, respectively. As examples of these calculations, we present oscillator strengths for the transitions 1 1S0–2 3P1, 2 1S0–2 3P1, 2 3S1–2 1P1, 2 1P1–3 3D1,2, and 2 3P1,2–3 1D2.

In this contribution to PSAS08 we report on the research activities developed in our Toulouse group in the framework of the BMV project, concerning the search for photon oscillations into massive particles, such as axion-like particles, in the presence of a strong transverse magnetic field. We recall our main result obtained in collaboration with LULI at École Polytechnique (Palaiseau, France). We also present the very preliminary results obtained with the BMV experiment which is set up at LNCMI (Toulouse, France).

Recent progress on the precision laser spectroscopy of antiprotonic helium atoms, as well as on the X-ray spectroscopy of kaonic helium atoms, are presented. These two may appear to be unrelated topics (except that both involve exotic helium atoms), but in fact a past study of kaonic helium system led to the serendipitous discovery of antiprotonic helium. Some historical background connecting these two exotic helium atoms, as well as future prospects, are discussed.

A comparison of precision frequency measurements to quantum electrodynamic (QED) theoretical predictions can be used to test theory and to obtain information regarding fundamental constants. We find that for Rydberg states, theoretical uncertainties due to the problematic nuclear size correction are very small. With the help of QED calculations, the largest remaining source of uncertainty can be eliminated. Theoretical predictions, taking advantage of the latest theoretical results, in combination with planned experiments, can lead to an improved value for the Rydberg constant.

We report on the measurement of the 2s-3s transition frequencies in the stable lithium isotopes and 2s-2p isotope shift measurements of 7,9,10,11Be, using a femtosecond frequency comb. For the beryllium isotopes, we extract the changes in the mean-square nuclear charge radius along the isotope chain by comparison with high-precision atomic mass shift calculations. The 2s-3s transition frequency is compared with theoretical calculations, and possibilities to extract an absolute value for the nuclear charge radius of lithium isotopes are discussed.

Studies of the M1-E2 interference effect in the Zeeman spectra of forbidden lines 459.7 and 564.0 nm of Bi I are reported. By the use of computer modelling techniques, the simulated contours were fitted to the recorded spectra to determine the electric-quadrupole admixture in forbidden lines. The E2 admixtures found are: (3.49 ± 0.35)% and (37.1 ± 1.8)% for 459.7 and 564.0 nm lines, respectively. Our results are compared with recent theories and other experiments.

We show that the non-spherical charge distribution of the proton manifests itself in hydrogen hyperfine splitting as an increase (in absolute value) of the proton Zemach radius and polarization contributions.

Precise isotope shift and fine structure measurements are critically reviewed. Each experiment was checked for whether the data found for different transitions yielded consistent values for the difference in mean-square nuclear charge radius Δr2 of 6,7Li. Experiments that passed this test found Δr2 = 0.735 ± 0.036, 0.755 ± 0.023, and 0.739 ± 0.013 fm2 by studying the Li+ 1s2s 3S→1s2p 3P transition, the Li D lines and the Li 2S1/2→3S1/2 transition, respectively. These data determine the difference in mean-square nuclear charge radius 25 times more accurately than electron scattering. Similarly, averaging the fine structure data from the same experiments gives 62 678.75 ± 0.55 MHz for the 7Li+ 1s2p 3P1–2 interval, in good agreement with theory. The results for the 6,7Li 2P fine structure intervals, 10 0.52.954 ± 0.049 and 10 053.154 ± 0.040 MHz, exceed computed values by 2 MHz and yield a splitting isotope shift, which is nearly a factor of 2 lower than a theoretical estimate.

Some years have passed since the report of the first production of cold antihydrogen by the Athena Collaboration and the Atrap Collaboration at CERN, but no clear answer has been given about the roles of the two mechanisms responsible for antihydrogen formation. A new preliminary analysis of the data acquired by the Athena Collaboration in different experimental conditions seems to suggest that three-body recombination mechanism is dominant in the first tens of seconds of the overlapping of the injected antiproton cloud with the positron plasma in the nested Penning trap, while radiative capture starts to become dominant afterwards.

Experimental tests of quantum electrodynamics (QED) have developed dramatically for simple systems of hydrogen and helium, but there has also been significant progress for medium-Z hydrogenic and helium-like atoms over the last few years. In this area, tests are often based on X-ray spectroscopic measurements, and here we review some key developments. Of particular interest is the status of few-electron QED in the medium-Z regime, the fine-structure Lamb shift from X-ray measurements, tests of two-electron QED, and of np subshell and excited state QED. We discuss some recent secondary tests of the data to confirm the quality and different approaches to experimental development to address the dominant systematics in this area.

Several properties are calculated for the first time for the B3Πg, C3Πu, A′5Σg+, and C″5Πu states of N2, i.e., quadrupole (Θ) and hexadecapole (Φ) moments, static dipole polarizability (α), and hyperfine structure (hfs) data such as the electric field gradient (qii) and magnetic Frosch–Foley parameters (b, c, d). These quantities are evaluated with the density functional theory (DFT) method B3LYP/aug-cc-pVQZ. The variation with geometry is also considered for all parameters above. The B(σgπg) and C(σuπg) triplet Π states have similar values of the anisotropy P|2|(2) ∝ (Pxx − Pyy), with P = Θii, qii, or Tii (dipolar hfs tensor). The first-order spin-orbit coupling constant AΛ and the second-order electron-spin g-shift Δg⊥ are obtained with a 6-311+G(2d) basis and multireference configuration interaction (MRDCI) wave functions. Values of AΛ calculated for W3Δu and (B, C, C′, C″) Π states reproduce well the experimental data (C and C′ are two different minima of 13Πu). The variation of AΛ with R(N-N) is regular for all states studied, except for AΠ(13Πu), which changes abruptly between the C and C′ minima (from 38 to 2 cm−1). The Δg⊥ values — evaluated via sum over states expansions — are calculated for A′5Σg+ as well as A3Σu+ and B′3Σu−. The spin-rotation constant γΣ is derived via Curl’s equation γΣ = (−2B)Δg⊥. We find γΣ(A′) to be negative and to decrease steadily with vibrational excitation, in line with experimental observations. Both Δg⊥ and γΣ of A′5Σg+ are determined by the coupling of this weakly bound state with the strongly repulsive 15Πg state.

We consider a Georgi–Glashow model conformally coupled to gravity. The conformally invariant action includes a triplet of scalar fields and SO(3) non-Abelian gauge fields. However, the usual mass term μ2ϕ2 is forbidden by the symmetry, and this role is now played by the conformal coupling of the Ricci scalar to the scalar fields. Spontaneous symmetry breaking occurs via gravitation. The spherically symmetric solutions correspond to localized solitons (magnetic monopoles) in asymptotically anti-de Sitter (AdS) spacetime and the metric outside the core of the monopole is found to be Schwarzschild–AdS. Though conformal symmetry excludes the Einstein–Hilbert term in the original action, it emerges in the effective action after spontaneous symmetry breaking and dominates the low-energy–long-distance regime outside the core of the monopole.

We consider the possibility of realizing inflation in nonlocal field theories containing infinitely many derivatives. Such constructions arise naturally in string field theory and also in a number of toy models, such as the p-adic string. After reviewing the complications (ghosts and instabilities) that arise when working with high-derivative theories, we discuss the the initial value problem and perturbative stability of theories with infinitely many derivatives. Next, we examine the inflationary dynamics and phenomenology of such theories. Nonlocal inflation can proceed even when the potential is naively too steep and generically predicts large non-Gaussianity in the cosmic microwave background.

After recalling some basing features of conformal field theory, we present an elementary introduction to the description of the states in the irreducible modules of the minimal models. The characters, which encode the state content of each module, are easily constructed from the representation theory of the Virasoro algebra and they take the form of infinite alternating sums. On the other hand, the relation between the minimal models and particular statistical models has led to the discovery of alternative expressions for the characters, which are positive definite. These entail a (yet to be fully worked out) quasi-particle description of the space of states, via a filling process with restrictions akin to the exclusion principle. The simplest class of positive characters, pertaining to the ℳ(2,p) models, is presented, and its underlying combinatorial aspects are spelled out. A natural conformal field theoretical interpretation of its quasi-particles is presented.

Various theories of quantum gravity argue that near the Planck scale, the Heisenberg uncertainty principle should be replaced by the so called generalized uncertainty principle (GUP). We show that the GUP gives rise to two additional terms in any quantum mechanical Hamiltonian, proportional to βp4 and β2p6, respectively, where β ∼ 1/(MPlc)2 is the GUP parameter. These terms become important at or above the Planck energy. Considering only the first of these and treating it as a perturbation, we show that the GUP affects the Lamb shift, Landau levels, reflection and transmission coefficients of a potential step and potential barrier, and the current in a scanning tunnel microscope (STM). Although these are too small to be measurable at present, we speculate on the possibility of extracting measurable predictions in the future.

We present an overview of recent progress in obtaining phenomenologically viable four-dimensional low-energy limits of the E8 × E8 heterotic string compactified on smooth non-simply connected Calabi–Yau threefolds. We briefly review the main steps of the construction and present two particular geometric models that lead to interesting four-dimensional phenomenology.

We clarify the role of Drinfeld doubles and κ-Poincaré symmetries in quantized (2+1)-gravity and Chern–Simons theory. We discuss the conditions under which a given Hopf algebra symmetry is compatible with a Chern–Simons theory and determine this compatibility explicitly for the Drinfeld doubles and κ-Poincaré symmetries associated with the isometry groups of (2+1)-gravity. In particular, we show that κ-Poincaré symmetries with a timelike deformation are not directly associated with (2+1)-gravity. The association between these κ-Poincaré symmetries and Chern–Simons theory is possible only in the de Sitter case and the relevant Chern–Simons theory is physically inequivalent to (2+1)-gravity.

Ideas related to the study of time-dependence in two dimensional Liouville string theory using the c=1 matrix model are reviewed. Following an introduction to Liouville string theory, the matrix model and the relationship between the two, an example of an exact quantum mechanical time-dependent solution is given. There is a brief discussion of the holographic issues complicating the construction of the exact spacetime interpretation of such solutions. An attempt is made to include sufficient background material to make the presentation self-contained and accessible to a non-expert.

We briefly review studies of off-shell stability of vacuum geometries in semiclassical gravity. We propose a study of off-shell stability of vacua in string theory by a distinct, though somewhat related approach, by studying their stability under suitable world-sheet sigma model renormalization group (RG) flows. Stability under RG flow is a mathematically well-posed and tractable problem in many cases, as we illustrate through examples. The advantage is that we can make definite predictions about late time behaviour and endpoints of off-shell processes in string theory.