Nonperturbative dynamics of scalar field theories through the Feynman-Schwinger representation

In this paper we present a summary of results obtained for scalar field theories using the Feynman-Schwinger (FSR) approach. Specifically, scalar QED and chi^2phi theories are considered. The motivation behind the applications discussed in this paper is to use the FSR method as a rigorous tool for testing the quality of commonly used approximations in field theory. Exact calculations in a quenched theory are presented for one-, two-, and three-body bound states. Results obtained indicate that some of the commonly used approximations, such as Bethe-Salpeter ladder summation for bound states and the rainbow summation for one body problems, produce significantly different results from those obtained from the FSR approach. We find that more accurate results can be obtained using other, simpler, approximation schemes.Comment: 25 pags, 19 figures, prepared for the volume celebrating the 70th birthday of Yuri Simono

Nonperturbative study of generalized ladder graphs in a \phi^2\chi theory

The Feynman-Schwinger representation is used to construct scalar-scalar bound states for the set of all ladder and crossed-ladder graphs in a \phi^2\chi theory in (3+1) dimensions. The results are compared to those of the usual Bethe-Salpeter equation in the ladder approximation and of several quasi-potential equations. Particularly for large couplings, the ladder predictions are seen to underestimate the binding energy significantly as compared to the generalized ladder case, whereas the solutions of the quasi-potential equations provide a better correspondence. Results for the calculated bound state wave functions are also presented.Comment: 5 pages revtex, 3 Postscripts figures, uses epsf.sty, accepted for publication in Physical Review Letter

Relativistic bound-state equations in three dimensions

Firstly, a systematic procedure is derived for obtaining three-dimensional bound-state equations from four-dimensional ones. Unlike ``quasi-potential approaches'' this procedure does not involve the use of delta-function constraints on the relative four-momentum. In the absence of negative-energy states, the kernels of the three-dimensional equations derived by this technique may be represented as sums of time-ordered perturbation theory diagrams. Consequently, such equations have two major advantages over quasi-potential equations: they may easily be written down in any Lorentz frame, and they include the meson-retardation effects present in the original four-dimensional equation. Secondly, a simple four-dimensional equation with the correct one-body limit is obtained by a reorganization of the generalized ladder Bethe-Salpeter kernel. Thirdly, our approach to deriving three-dimensional equations is applied to this four-dimensional equation, thus yielding a retarded interaction for use in the three-dimensional bound-state equation of Wallace and Mandelzweig. The resulting three-dimensional equation has the correct one-body limit and may be systematically improved upon. The quality of the three-dimensional equation, and our general technique for deriving such equations, is then tested by calculating bound-state properties in a scalar field theory using six different bound-state equations. It is found that equations obtained using the method espoused here approximate the wave functions obtained from their parent four-dimensional equations significantly better than the corresponding quasi-potential equations do.Comment: 28 pages, RevTeX, 6 figures attached as postscript files. Accepted for publication in Phys. Rev. C. Minor changes from original version do not affect argument or conclusion

Neurotransmitters as food supplements: the effects of GABA on brain and behavior

Gamma-aminobutyric acid (GABA) is the main inhibitory neurotransmitter in the human cortex. The food supplement version of GABA is widely available online. Although many consumers claim that they experience benefits from the use of these products, it is unclear whether these supplements confer benefits beyond a placebo effect. Currently, the mechanism of action behind these products is unknown. It has long been thought that GABA is unable to cross the blood–brain barrier (BBB), but the studies that have assessed this issue are often contradictory and range widely in their employed methods. Accordingly, future research needs to establish the effects of oral GABA administration on GABA levels in the human brain, for example using magnetic resonance spectroscopy. There is some evidence in favor of a calming effect of GABA food supplements, but most of this evidence was reported by researchers with a potential conflict of interest. We suggest that any veridical effects of GABA food supplements on brain and cognition might be exerted through BBB passage or, more indirectly, via an effect on the enteric nervous system. We conclude that the mechanism of action of GABA food supplements is far from clear, and that further work is needed to establish the behavioral effects of GABA

Role of retardation in 3-D relativistic equations

Equal-time Green's function is used to derive a three-dimensional integral equation from the Bethe-Salpeter equation. The resultant equation, in the absence of anti-particles, is identical to the use of time-ordered diagrams, and has been used within the framework of $\phi^2\sigma$ coupling to study the role of energy dependence and non-locality when the two-body potential is the sum of $\sigma$-exchange and crossed $\sigma$ exchange. The results show that non-locality and energy dependence make a substantial contribution to both the on-shell and off-shell amplitudes.Comment: 17 pages, RevTeX; 8 figures. Accepted for publication in Phys. Rev. C56 (Nov. 97

Variational Worldline Approximation for the Relativistic Two-Body Bound State in a Scalar Model

We use the worldline representation of field theory together with a variational approximation to determine the lowest bound state in the scalar Wick-Cutkosky model where two equal-mass constituents interact via the exchange of mesons. Self-energy and vertex corrections are included approximately in a consistent way as well as crossed diagrams. Only vacuum-polarization effects of the heavy particles are neglected. In a path integral description of an appropriate current-current correlator an effective, retarded action is obtained by integrating out the meson field. As in the polaron problem we employ a quadratic trial action with variational functions to describe retardation and binding effects through multiple meson exchange.The variational equations for these functions are derived, discussed qualitatively and solved numerically. We compare our results with the ones from traditional approaches based on the Bethe-Salpeter equation and find an enhanced binding contrary to some claims in the literature. For weak coupling this is worked out analytically and compared with results from effective field theories. However, the well-known instability of the model, which usually is ignored, now appears at smaller coupling constants than in the one-body case and even when self-energy and vertex corrections are turned off. This induced instability is investigated analytically and the width of the bound state above the critical coupling is estimated.Comment: 62 pages, 7 figures, FBS style, published versio

De vooruitziende blik van de Groot

Study success rates in higher education were already described in an article in Pedagogische Studien in 1959. Professor A.D. de Groot, internationally well-known by his research on Thought and choice in chess, analysed the success rate figures provided by Statistics Netherlands. Based on the differences in success rates between students with different profiles in pre-university education, between genders and between students from different social-economic backgrounds, he formulated some concerns in the case much more students should enrol in universities, such as lower success rates and longer time to degree. He warned to exercise restraint in selecting students based on group statistics of successful characteristics. Since this article was published, universities are still struggling with the question how to raise the success rates. De Groot's concerns are still in the middle of all the discussions and policy in Dutch higher education, at the moment especially pointing at selection methods. All in all we can conclude that after 54 years there is still work to do

The Impact of Donor and Recipient Genetic Variation on Outcomes After Solid Organ Transplantation:a Scoping Review and Future Perspectives

At the outset of solid organ transplantation, genetic variation between donors and recipients was recognized as a major player in mechanisms such as allograft tolerance and rejection. Genome-wide association studies have been very successful in identifying novel variant-trait associations, but have been difficult to perform in the field of solid organ transplantation due to complex covariates, era effects, and poor statistical power for detecting donor-recipient interactions. To overcome a lack of statistical power, consortia such as the International Genetics and Translational Research in Transplantation Network have been established. Studies have focused on the consequences of genetic dissimilarities between donors and recipients and have reported associations between polymorphisms in candidate genes or their regulatory regions with transplantation outcomes. However, knowledge on the exact influence of genetic variation is limited due to a lack of comprehensive characterization and harmonization of recipients' or donors' phenotypes and validation using an experimental approach. Causal research in genetics has evolved from agnostic discovery in genome-wide association studies to functional annotation and clarification of underlying molecular mechanisms in translational studies. In this overview, we summarize how the recent advances and progresses in the field of genetics and genomics have improved the understanding of outcomes after solid organ transplantation

Restoration of rotational invariance of bound states on the light front

We study bound states in a model with scalar nucleons interacting via an exchanged scalar meson using the Hamiltonian formalism on the light front. In this approach manifest rotational invariance is broken when the Fock space is truncated. By considering an effective Hamiltonian that takes into account two meson exchanges, we find that this breaking of rotational invariance is decreased from that which occurs when only one meson exchange is included. The best improvement occurs when the states are weakly bound.Comment: 20 pages, 6 figures, uses feynMF; changed typos, clarified use of angular momentu