Bose-Einstein condensation (BEC) has been observed in a dilute gas of sodium atoms. A Bose-Einstein condensate consists of a macroscopic population of the ground state of the system, and is a coherent state of matter. In an ideal gas, this phase transition is purely quantum-statistical. The study of BEC in weakly interacting systems which can be controlled and observed with precision holds the promise of revealing new macroscopic quantum phenomena that can be understood from first principles.

Bose-Einstein condensation in a gas of sodium atoms

We have studied the three quark system in a relativized version of the quark potential model with chromodynamics. With parameters consistent with those of an analogous study of meson spectroscopy we obtain a successful description of the spectrum of baryons. The model naturally explains the apparent absence of spin‐orbit interactions in baryons.

Baryons in a relativized quark model with chromodynamics

THE subject of quantum electrodynamics is extremely difficult, even for the case of a single electron. The usual method of solving the corresponding wave equation leads to divergent integrals. To avoid these, Prof. P. A. M. Dirac* uses the method of redundant variables. This does not abolish the difficulty, but presents it in a new form, which may be dealt with in two ways. The first of these needs only comparatively simple mathematics and is directly connected with an elegant general scheme, but unfortunately its wave functions apply only to a hypothetical world and so its physical interpretation is indirect. The second way has the advantage of a direct physical interpretation, but the mathematics is so complicated that it has not yet been solved even for what appears to be the simplest possible case. Both methods seem worth further study, failing the discovery of a third which would combine the advantages of both.

http://ieeexplore.ieee.org/iel5/3/22993/01069961.pdf

Quantum electrodynamics

The authors review the relation between the inflationary potential and the spectra of density waves (scalar perturbations) and gravitational waves (tensor perturbations) produced, with particular emphasis on the possibility of reconstructing the inflaton potential from observations. The spectra provide a potentially powerful test of the inflationary hypothesis; they are not independent but instead are linked by consistency relations reflecting their origin from a single inflationary potential. To lowest order in a perturbation expansion there is a single, now familiar, relation between the tensor spectral index and the relative amplitude of the spectra. The authors demonstrate that there is an infinite hierarchy of such consistency equations, though observational difficulties suggest only the first is ever likely to be useful. They also note that since observations are expected to yield much better information on the scalars than on the tensors, it is likely to be the next-order version of this consistency equation that will be appropriate, not the lowest-order one. If inflation passes the consistency test, one can then confidently use the remaining observational information to constrain the inflationary potential, and the authors survey the general perturbative scheme for carrying out this procedure. Explicit expressions valid to next-lowest order in the expansion are presented. The prospects for future observations' reaching the quality required are then briefly assessed and simulated data sets motivated by this outlook are considered.

https://arxiv.org/pdf/astro-ph/9508078.pdf

Reconstructing the inflaton potential—an overview

Using our previously developed crossing and duality consistent model for kaon photoproduction and radiative capture, we investigate the kaon electroproduction processes p(e,e'${\mathit{K}}^{+}$)Y for Y=\ensuremath{\Lambda}, ${\mathrm{\ensuremath{\Sigma}}}^{0}$, and \ensuremath{\Lambda}(1405). Because there is no electroproduction data near threshold, consistency requires extending the energy range of our photoproduction model parametrization from an upper bound of ${\mathit{E}}_{\ensuremath{\gamma}}^{\mathrm{lab}}$=1.4 to 2.2 GeV. We find that baryon resonances with spin greater than 1/2 are necessary to describe the higher energy photoproduction data (1.4\ensuremath{\le}${\mathit{E}}_{\ensuremath{\gamma}}^{\mathrm{lab}}$\ensuremath{\le}2.2 GeV). We also extend our use of duality by representing these higher-spin s- and u-channel baryon resonances with the low-lying t-channel vector, ${\mathit{K}}^{\mathrm{*}}$(890), and pseudovector, ${\mathit{K}}_{1}$(1270), mesons. Using this extended crossing and duality consistent model, we obtain reasonable agreement with the data for both photoproduction and electroproduction processes.

Hyperon electroproduction in a crossing and duality constrained model.

The photon-decay amplitudes and widths of the low-lying strange baryons are calculated within the framework of the nonrelativistic quark model of Isgur and Karl. A comparison with experiment is made.

Photon decays of baryons with strangeness

The Gaussian variational approximation is used to calculate the two-particle bound-state binding energy and wave function in the model: $\ensuremath{\lambda}({\ensuremath{\varphi}}^{6}\ensuremath{-}{\ensuremath{\varphi}}^{4})$: in 1 + 1 dimensions. An analytic result is compared to the perturbative calculation of Dimock and Eckmann and to the numerical, lattice work of Barnes and Daniell.

Variational calculation of the bound-state wave function in :λ(φ 6 -φ 4 ) 2 :

We consider particle-antiparticle bound states in the scalar Yukawa (Wick-Cutkosky) model. The variational method in the Hamiltonian formalism of quantum field theory is employed. A reformulation of the model is studied, in which covariant Green functions are used to solve for the mediating field in terms of the particle fields. A simple Fock-state variational ansatz is used to derive a relativistic equation for the particle-antiparticle states. This equation contains one-quantum-exchange and virtual-annihilation interactions. It is shown that analytic solutions of this equation can be obtained for the simplified case where only the virtual-annihilation interaction is retained. More generally, numerical and perturbative solutions of the equation are obtained for the massive and massless exchange cases. We compare our results with various Bethe-Salpeter-based calculations.

A variational calculation of particle-antiparticle bound states in the scalar Yukawa model

We consider a reformulation of quantum electrodynamics in which covariant Green functions are used to solve for the electromagnetic field in terms of the fermion fields. The resulting modified Hamiltonian contains the photon propagator directly. A simple Fock-state variational trial function is used to derive relativistic two-fermion equations variationally from the expectation value of the Hamiltonian of the field theory. The interaction kernel of the equation is shown to be, in essence, the invariant M matrix in lowest order. Solutions of the two-body equations are presented for muoniumlike systems for small coupling strengths. The results compare well with the observed muonium spectrum, as well as that for hydrogen and muonic hydrogen. Anomalous magnetic moment effects are discussed.

Variational two-fermion wave equations in quantum electrodynamics: Muoniumlike systems

The radiative annihilations of ${K}^{\mathrm{\ensuremath{-}}}$p atoms to \ensuremath{\Lambda}\ensuremath{\gamma} and ${\ensuremath{\Sigma}}^{0}$\ensuremath{\gamma} are shown to be dominated by the \ensuremath{\Lambda}(1405) hyperon. These processes thus provide a sensitive probe of the properties of this controversial state. We show that present data on the \ensuremath{\Lambda}\ensuremath{\gamma} branching ratio are in agreement with its interpretation as a normal quark-model state, and that further information on the \ensuremath{\Lambda}\ensuremath{\gamma} and the comparably strong ${\ensuremath{\Sigma}}^{0}$\ensuremath{\gamma} channel will provide compelling tests of the viability of this versus the K\ifmmode\bar\else\textasciimacron\fi{}N bound-state interpretation.

Jurij W. Darewych

Papers

Photon decays of baryons with strangeness

Variational calculation of the bound-state wave function in :λ(φ 6 -φ 4 ) 2 :

A variational calculation of particle-antiparticle bound states in the scalar Yukawa model

Variational two-fermion wave equations in quantum electrodynamics: Muoniumlike systems

Radiative annihilation of K-p atoms and the Lambda (1405).