SOLVING THE BETHE--SALPETER EQUATION IN MINKOWSKI SPACE: SCALAR THEORIES

The Bethe-Salpeter (BS) equation for scalar-scalar bound states in scalar theories without derivative coupling is formulated and solved in Minkowski space. This is achieved using the perturbation theory integral representation (PTIR), which allows these amplitudes to be expressed as integrals over weight functions and known singularity structures and hence allows us to convert the BS equation into an integral equation involving weight functions. We obtain numerical solutions using this formalism for a number of scattering kernels to illustrate the generality of the approach. It applies even when the na\"{\i}ve Wick rotation is invalid. As a check we verify, for example, that this method applied to the special case of the massive ladder exchange kernel reproduces the same results as are obtained by Wick rotation.Comment: 8 pages, regular latex, no figures. Entire manuscript available as a ps file at http://www.physics.adelaide.edu.au/theory/home.html Also available via anonymous ftp at ftp://adelphi.adelaide.edu.au/pub/theory/ADP-95-28.T182.p

Ion-induced nucleation. II. Polarizable multipolar molecules

Density functional theory is applied to ion-induced nucleation of polarizable multipolar molecules. The asymmetric nature of the ion-molecule interaction is shown to cause the sign preference in ion-induced nucleation. When the ion-molecule interaction is weak, the observed sign preference is consistent with that of the bare ion-molecule interaction potential and decreases with increasing supersaturation. However, as the ion-molecule interaction becomes stronger, the sign preference in the reversible work exhibits some nontrivial behavior. For molecular parameters applicable for CS2 and CH4, the predicted values of the reversible work of nucleation depend on the sign of the ion charge, yielding a difference in the nucleation rate by factors of 10 to 10^(2) and 10 to 10^(5), respectively

Ion-induced nucleation: A density functional approach

Density functional theory is applied to ion-induced nucleation of dipolar molecules. The predicted reversible work shows a sign preference, resulting in a difference in the nucleation rate by a factor of 10–10^2, for realistic values of model parameters. The sign effect is found to decrease systematically as the supersaturation is increased. The asymmetry of a molecule is shown to be directly responsible for the sign preference in ion-induced nucleation

Binary nucleation of sulfuric acid-water: Monte Carlo simulation

We have developed a classical mechanical model for the H2SO4/H2O binary system. Monte Carlo simulation was performed in a mixed ensemble, in which the number of sulfuric acid molecules is fixed while that of water molecules is allowed to fluctuate. Simulation in this ensemble is computationally efficient compared to conventional canonical simulation, both in sampling very different configurations of clusters relevant in nucleation and in evaluating the free energy of cluster formation. The simulation yields molecular level information, such as the shape of the clusters and the dissociation behavior of the acid molecule in the cluster. Our results indicate that the clusters are highly nonspherical as a result of the anisotropic intermolecular interactions and that a cluster with a given number of acid molecules has several very different conformations, which are close in free energy and hence equally relevant in nucleation. The dissociation behavior of H2SO4 in a cluster differs markedly from that in bulk solution and depends sensitively on the assumed value of the free energy f(hb) of the dissociation reaction H2SO4+H2O-HSO4-. H3O+. In a small cluster, no dissociation is observed. As the cluster size becomes larger, the probability of having an HSO4-. H3O+ ion pair increases. However, in clusters relevant in nucleation, the resulting ion pairs remain in contact; about 240 water molecules are required to observe behavior that resembles that in bulk solution. If a larger value of f(hb) is assumed to reflect its uncertainty, the probability of dissociation becomes negligible. A reversible work surface obtained for a condition typical of vapor to liquid nucleation suggests that the rate-limiting step of new particle formation is a binary collision of two hydrated sulfuric acid molecules. The ion pairs formed by dissociation play a key role in stabilizing the resulting cluster. The reversible work surface is sensitive to the assumed value of f(hb), thus pointing to the need for an accurate estimate of the quantity either by ab initio calculations or experiments

Solving the Bethe-Salpeter equation for bound states of scalar theories in Minkowski space

We apply the perturbation theory integral representation (PTIR) to solve for the bound state Bethe-Salpeter (BS) vertex for an arbitrary scattering kernel, without the need for any Wick rotation. The results derived are applicable to any scalar field theory (without derivative coupling). It is shown that solving directly for the BS vertex, rather than the BS amplitude, has several major advantages, notably its relative simplicity and superior numerical accuracy. In order to illustrate the generality of the approach we obtain numerical solutions using this formalism for a number of scattering kernels, including cases where the Wick rotation is not possible.Comment: 28 pages of LaTeX, uses psfig.sty with 5 figures. Also available via WWW at http://www.physics.adelaide.edu.au/theory/papers/ADP-97-10.T248-abs.html or via anonymous ftp at ftp://bragg.physics.adelaide.edu.au/pub/theory/ADP-97-10.T248.ps A number of (crucial) typographical errors in Appendix C corrected. To be published in Phys. Rev. D, October 199

Does the effective Lagrangian for low-energy QCD scale?

QCD is not an approximately scale invariant theory. Hence a dilaton field is not expected to provide a good description of the low-energy dynamics associated with the gluon condensate. Even if such a field is introduced, it remains almost unchanged in hadronic matter at normal densities. This is because the large glueball mass together with the size of the phenomenological gluon condensate ensure that changes to that condensate are very small at such densities. Any changes in hadronic masses and decay constants in matter generated by that condensate will be much smaller that those produced directly by changes in the quark condensate. Hence masses and decay constants are not expected to display a universal scaling.Comment: 7 pages (RevTeX), MC/TH 94/0

Serum-induced changes in the physiology of mammalian retinal glial cells: role of lysophosphatidic acid

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65571/1/j.1469-7793.1998.445bw.x.pd

Study of relativistic bound states for scalar theories in Bethe-Salpeter and Dyson-Schwinger formalism

The Bethe-Salpeter equation for Wick-Cutkosky like models is solved in dressed ladder approximation. The bare vertex truncation of the Dyson-Schwinger equations for propagators is combined with the dressed ladder Bethe-Salpeter equation for the scalar S-wave bound state amplitudes. With the help of spectral representation the results are obtained directly in Minkowski space. We give a new analytic formula for the resulting equation simplifying the numerical treatment. The bare ladder approximation of Bethe-Salpeter equation is compared with the one with dressed ladder. The elastic electromagnetic form factors is calculated within the relativistic impulse approximation.Comment: 30 pages, 10 figures, accepted for publication in Phys. Rev.