1,370 research outputs found
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
Refinement Type Inference via Horn Constraint Optimization
We propose a novel method for inferring refinement types of higher-order
functional programs. The main advantage of the proposed method is that it can
infer maximally preferred (i.e., Pareto optimal) refinement types with respect
to a user-specified preference order. The flexible optimization of refinement
types enabled by the proposed method paves the way for interesting
applications, such as inferring most-general characterization of inputs for
which a given program satisfies (or violates) a given safety (or termination)
property. Our method reduces such a type optimization problem to a Horn
constraint optimization problem by using a new refinement type system that can
flexibly reason about non-determinism in programs. Our method then solves the
constraint optimization problem by repeatedly improving a current solution
until convergence via template-based invariant generation. We have implemented
a prototype inference system based on our method, and obtained promising
results in preliminary experiments.Comment: 19 page
Adhesion and spreading of cultured endothelial cells on modified and unmodified poly(ethylene terephthalate): a morphological study
The in vitro adhesion and spreading of human endothelial cells (HEC) on hydrophobic poly(ethylene terephthalate) (PETP) and moderately wettable tissue culture polyethylene terephthalate) (TCPETP) were studied with light microscopy and electron microscopy. Numbers of HEC adhering on TCPETP were always higher than those found on PETP. When cells were seeded in the presence of serum, extensive cell spreading on both PETP and TCPETP was observed after the first 30 min. Thereafter, spread cells appeared to withdraw from the PETP surface, resulting in irregularly shaped cells. Complete cell spreading occurred on TCPETP. Complete cell spreading also occurred on PETP and TCPETP when HEC had first been seeded from phosphate buffer solution and serum was supplied after 30 min. Furthermore, HEC spread on both PETP and TCPETP when the surfaces were precoated with protein(s), which promotes cell adhesion. However, when plasma was used for the coating, spread cells did not proliferate in a monolayer pattern. This study shows that TCPETP is, in general, a better surface for adhesion and proliferation of HEC than is PETP, suggesting that vascular prostheses with a TCPETP-like surface will perform better in vivo than prostheses made of PETP
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
The Role of the Noradrenergic System in the Exploration–Exploitation Trade-Off: A Psychopharmacological Study
Animal research and computational modeling have indicated an important role for the neuromodulatory locus coeruleus–norepinephrine (LC–NE) system in the control of behavior. According to the adaptive gain theory, the LC–NE system is critical for optimizing behavioral performance by regulating the balance between exploitative and exploratory control states. However, crucial direct empirical tests of this theory in human subjects have been lacking. We used a pharmacological manipulation of the LC–NE system to test predictions of this theory in humans. In a double-blind parallel-groups design (N = 52), participants received 4 mg reboxetine (a selective norepinephrine reuptake inhibitor), 30 mg citalopram (a selective serotonin reuptake inhibitor), or placebo. The adaptive gain theory predicted that the increased tonic NE levels induced by reboxetine would promote task disengagement and exploratory behavior. We assessed the effects of reboxetine on performance in two cognitive tasks designed to examine task (dis)engagement and exploitative versus exploratory behavior: a diminishing-utility task and a gambling task with a non-stationary pay-off structure. In contrast to predictions of the adaptive gain theory, we did not find differences in task (dis)engagement or exploratory behavior between the three experimental groups, despite demonstrable effects of the two drugs on non-specific central and autonomic nervous system parameters. Our findings suggest that the LC–NE system may not be involved in the regulation of the exploration–exploitation trade-off in humans, at least not within the context of a single task. It remains to be examined whether the LC–NE system is involved in random exploration exceeding the current task context
First-Order Logic Theorem Proving and Model Building via Approximation and Instantiation
In this paper we consider first-order logic theorem proving and model
building via approximation and instantiation. Given a clause set we propose its
approximation into a simplified clause set where satisfiability is decidable.
The approximation extends the signature and preserves unsatisfiability: if the
simplified clause set is satisfiable in some model, so is the original clause
set in the same model interpreted in the original signature. A refutation
generated by a decision procedure on the simplified clause set can then either
be lifted to a refutation in the original clause set, or it guides a refinement
excluding the previously found unliftable refutation. This way the approach is
refutationally complete. We do not step-wise lift refutations but conflicting
cores, finite unsatisfiable clause sets representing at least one refutation.
The approach is dual to many existing approaches in the literature because our
approximation preserves unsatisfiability
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
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.
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