### 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 •

abstract

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 •

abstract

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 •

abstract

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 •

abstract

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 •

abstract

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 •

abstract

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 •

abstract

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.

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