The Role of Boundary Conditions in Solving Finite-Energy, Two-Body, Bound-State Bethe-Salpeter Equations

The difficulties that typically prevent numerical solutions from being obtained to finite-energy, two-body, bound-state Bethe-Salpeter equations can often be overcome by expanding solutions in terms of basis functions that obey the boundary conditions. The method discussed here for solving the Bethe-Salpeter equation requires only that the equation can be Wick rotated and that the two angular variables associated with rotations in three-dimensional space can be separated, properties that are possessed by many Bethe-Salpeter equations including all two-body, bound-state Bethe-Salpeter equations in the ladder approximation. The efficacy of the method is demonstrated by calculating finite-energy solutions to the partially-separated Bethe-Salpeter equation describing the Wick-Cutkosky model when the constituents do not have equal masses.Comment: 18 page

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

COVARIANT SINGLE-TIME BOUND-STATE EQUATION

We derive a system of covariant single-time equations for a two-body bound state in a model of scalar fields $\phi_1$ and $\phi_2$ interacting via exchange of another scalar field $\chi$. The derivation of the system of equations follows from the Haag expansion. The equations are linear integral equations that are explicitly symmetric in the masses, $m_1$ and $m_2$, of the scalar fields, $\phi_1$ and $\phi_2$. We present an approximate analytic formula for the mass eigenvalue of the ground state and give numerical results for the amplitudes for a choice of constituent and exchanged particle masses.Comment: 8 pages latex; 4 figures uuencoded ps fil

Survey of electroencephalography usage and techniques for dogs

BackgroundCanine epilepsy is a chronic common neurologic condition where seizures may be underreported. Electroencephalography (EEG) is the patient-side test providing an objective diagnostic criterion for seizures and epilepsy. Despite this, EEG is thought to be rarely used in veterinary neurology.ObjectivesThis survey study aims to better understand the current canine EEG usage and techniques and barriers in veterinary neurology.MethodsThe online Qualtrics link was distributed via listserv to members of the American College of Veterinary Internal Medicine (ACVIM) Neurology Specialty and the European College of Veterinary Neurology (ECVN), reaching at least 517 veterinary neurology specialists and trainees worldwide.ResultsThe survey received a 35% response rate, for a total of 180 participant responses. Fewer than 50% of veterinary neurologists are currently performing EEG and it is performed infrequently. The most common indication was to determine a discrete event diagnosis. Other reasons included monitoring treatment, determining brain death, identifying the type of seizure or epilepsy, localizing foci, sleep disorders, for research purposes, and post-op brain surgery monitorization. Most respondents interpreted their own EEGs. Clinical barriers to the performance of EEG in dogs were mainly equipment availability, insufficient cases, and financial costs to clients.ConclusionThis survey provides an update on EEG usage and techniques for dogs, identifying commonalities of technique and areas for development as a potential basis for harmonization of canine EEG techniques. A validated and standardized canine EEG protocol is hoped to improve the diagnosis and treatment of canine epilepsy

Solving the Bethe-Salpeter Equation for Scalar Theories in Minkowski Space

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: 23 pages with 3 uuencoded, compressed Postscript figures. Entire manuscript available as a ps file at http://www.physics.adelaide.edu.au/theory/home.html . Also available at ftp://adelphi.adelaide.edu.au/pub/theory/ADP-94-24.T164.p

Deep Inelastic Structure Functions in a Covariant Spectator Model

Deep-inelastic structure functions are studied within a covariant scalar diquark spectator model of the nucleon. Treating the target as a two-body bound state of a quark and a scalar diquark, the Bethe-Salpeter equation (BSE) for the bound state vertex function is solved in the ladder approximation. The valence quark distribution is discussed in terms of the solutions of the BSE.Comment: 22 pages, LaTeX, 7 Postscript figures included using epsfig.st