Precision is given to the concept of electronegativity. It is the negative of the chemical potential (the Lagrange multiplier for the normalization constraint) in the Hohenberg–Kohn density functional theory of the ground state: χ=−μ=−(∂E/∂N)v. Electronegativity is constant throughout an atom or molecule, and constant from orbital to orbital within an atom or molecule. Definitions are given of the concepts of an atom in a molecule and of a valence state of an atom in a molecule, and it is shown how valence‐state electronegativity differences drive charge transfers on molecule formation. An equation of Gibbs–Duhem type is given for the change of electronegativity from one situation to another, and some discussion is given of certain relations among energy components discovered by Fraga.

Electronegativity: The density functional viewpoint

Singular Integral Equations. By N.I. Muskhelishvili. Translated fromthe 2nd Russian edition by J.R.M. Radok. Pp. 447. F1. 28.50. 1953. (Noordhoff, Groningen)

Annals of physics

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

http://cds.cern.ch/record/307205/files/arXiv:hep-ph_9607355.pdf

Radiative energy loss of high-energy quarks and gluons in a finite volume quark - gluon plasma

We discuss a new method to perform numerical simulations of one-dimensional systems with fermion and boson degrees of freedom. The method is based on a direct-space, imaginary-time representation of the fermion field. It is fast so that systems having up to 100 sites can easily be simulated. In addition, the method provides an intuitive physical "picture" of the ground state of a one-dimensional many-body system. We discuss in detail how to implement the method and how to compute various physical quantities. In particular, we show how to extend the method to study averages of off-diagonal quantities in an occupation-number representation. To assess the accuracy of our procedure, we apply it to free fermions in one dimension and compare with exact results. We then study a model of spinless interacting fermions and obtain the expected phase structure and behavior of correlation functions. We also consider the extended Hubbard model at various points in its phase diagram and study the behavior of spin-density, charge-density, and pairing correlation functions. We then study the Gross-Neveu model and show how the behavior depends on the number of fermion flavors. Finally, we consider an electron-phonon model and study its behavior both in the one-particle polaron sector and in the half-filled-band case. Along the way we show pictures of the ground-state configurations that give physical insight into the properties of the systems, like charge-density-wave, spin-density-wave, and superconducting states, "fractional charges," and solitons. We conclude by comparing our method with other methods and discuss the possibility of extending it to higher dimensions.

Monte Carlo Simulations of One-dimensional Fermion Systems

Large transverse momentum processes

A new Monte Carlo approach applicable to systems with fermion and boson degrees of freedom is proposed. The main advantage of the method is its speed: For systems in one space and one time dimension (1 + 1) the calculation reduces to doing Monte Carlo computations on a two-dimensional classical system with local interactions. Here the potential of the method is illustrated by application to various (1 + 1)-dimensional systems.

Efficient Monte Carlo Procedure for Systems with Fermions

The constituent-interchange model is used to relate large- and small-momentum-transfer reactions, to relate inclusive and exclusive processes, and to predict the form of the inclusive cross section throughout the Peyrou plot. Two important corrections to the triple-Regge formula are derived. The first, important at a small missing mass, allows a smooth connection to exclusive processes. The second, important at large missing mass, allows a smooth connection to the central region and to the large-transverse-momentum regime. Simple quark-counting rules are given which predict the limiting behavior of Regge trajectories and residue functions, and also the powers of ${{P}_{T}}^{2}$ and the missing-mass dependence of inclusive cross sections. Many experimental consequences of the model are given.

/pdf/unified-description-of-inclusive-and-exclusive-reactions-at-15impeoeje.pdf

Unified Description of Inclusive and Exclusive Reactions at All Momentum Transfers

The Landau-Pomeranchuk-Migdal effect is the suppression of Bethe-Heitler radiation caused by multiple scattering in the target medium. In this paper, the quantum treatment given earlier for finite but homogeneous targets is extended to structured targets. It is shown that radiators composed of separated plates or of a medium with a varying radiation length can exhibit coherence maxima and minima in their photon spectra.

/pdf/structured-targets-and-the-landau-pomeranchuk-migdal-effect-2shp69dj75.pdf

Richard Blankenbecler

Papers

Monte Carlo Simulations of One-dimensional Fermion Systems

Large transverse momentum processes

Efficient Monte Carlo Procedure for Systems with Fermions

Unified Description of Inclusive and Exclusive Reactions at All Momentum Transfers

Structured targets and the Landau-Pomeranchuk-Migdal effect