Regular Series

Vol. 21 (1990), No. 10, pp. 755 – 839

On the Newtonian Limit of General Relativity

Acta Phys. Pol. B 21, 755 (1990)

page 755 •


The relations between the Newton–Cartan theory, Newton’s classical gravitational theory and General Relativity are discussed. It is shown that the limit \(c \to \infty \) of General Relativity becomes identical with the Newton–Cartan theory, provided the so-called time function — defined as proportional to the singular part of the covariant Einsteinian metric in the transition \(c \to \infty \) — satisfies a certain boundary condition at spatial infinity. Using this limiting process, one obtains an asymptotic representation of Einsteinian fields “near” the Newtonian limit. This should allow us to identify post-Newtonian corrections for the Newton–Cartan theory.

Birkhoff’s Theorem in the Generalized Field Theory

Acta Phys. Pol. B 21, 767 (1990)

page 767 •


It is shown that, contrary to previous expectations, Birkhoff’s theorem is valid in the Generalized Field Theory.

The Decoupling Theorem and the Pauli–Villars Regularization

Acta Phys. Pol. B 21, 775 (1990)

page 775 •


It is shown how the Pauli–Villars regularization method is affected by the violation of the Appelquist–Carazzone decoupling theorem.

Semigroup of \(N = 1,\) 2 Superconformal Transformations and Conformal Superfields

Acta Phys. Pol. B 21, 783 (1990)

page 783 •


All possible \(N = 1\) and \(N = 2\) superconformal transformations are presented and classified into two (for \(N = 1\)) and three (for \(N = 2\)) types. Only the first one corresponds to the superconformal group, all others are elements of a semigroup. They are noninvertible and do not admit an infinitesimal form. The set of them is the ideal of the full superconformal semigroup. The permanent is used when classifying \(N = 2\) superconformal transformations and finding the \(N = 2\) Berezinian. Also the transformations from \(N = 1\) to \(N = 2\) and from \(N = 2\) to \(N = 1\) are found. The structure of the superfields which are conformal outside super Riemann surface is obtained.

Comparison of Space of the Composite Fermions Model with Superspace

Acta Phys. Pol. B 21, 813 (1990)

page 813 •


Two types of extension of the Minkowski space-time are compared. It is shown that the composite fermions model can be considered in (\(N = 2\))-superspace without torsion, with additional coordinates transforming independently from main coordinates. A set of supermanifolds corresponds to a set of solutions of the model. Their number and character of constraints determine an internal symmetry group, while in supersymmetrical models this group is determined by the extension degree \(N\). Use of anticommuting coordinates leads to appearance of scalar SU(2)-doublets in the model.

On the Distribution of the Compound-Nucleus Resonances

Acta Phys. Pol. B 21, 819 (1990)

page 819 •


The problem of distribution of the spacing of compound nucleus resonances is studied by using an identity which expresses a determinant in terms of the trace of log of the matrix. An explicit connection between the two-point correlation function and the fluctuation property of Gaussian Orthogonal Ensemble is shown.

A Thomas-Fermi Model of Localization of Proton Impurities in Neutron Matter

Acta Phys. Pol. B 21, 823 (1990)

page 823 •


We show that the proton impurity in a neutron matter can create an inhomogeneity in density which acts as a potential well localizing the proton’s wave function. At low densities this inhomogeneity is a neutron bulge, whereas at high densities a neutron deficiency (bubble) occurs. We calculate variationally the proton’s energy using a Gaussian wave function. The neutron background is treated in a Thomas–Fermi approximation. The Skyrme interactions are used. We find that the localized proton has lower energy than the plane wave proton for densities below the lower critical density \(n_1 \cong 0.3n_0\), and above the upper critical density \(n_{\rm u} \cong 2.2n_0\), where \(n_0 = 0.17\) fm\(^{-3}\). We discuss some implications of the proton localization for magnetic properties of neutron matter containing a small admixture of protons.


ver. 2021.06.25 • we use cookies and MathJax