Hypersurfaces of constant mean extrinsic curvature

ANNALS

OF PHYSICS

132, 482-483 (1981)

Abstracts

of Papers

to Appear

in Future

Issues

Problem in Classical Electrodynamics and the “Casimir Theorem.” B. BOSCO, Istituto di Fisica Teorica dell’universitfi di Firenze, Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, Italy; AND M. T. SACCHI, Istituto di Fisica e Fisica Tecnica, Facoltfi di Architettura dell’Universit8 di Firenze, Italy.

On the Inversion

The inversion problem in classical electrodynamics is investigated in great detail in connection with the “Casimir theorem” which states that given all multipoles (both electric and magnetic) of a given charge and current distribution localized in a finite region, the electromagnetic field outside the region will not be sufficient to determine uniquely such a distribution. We wish to determine whether supplementary conditions exist which allow a determination of such distribution. We show that if the system contains only currents and charges (no magnetization) the divergences of the currents will allow such a determination. A similar result holds if the system contains only magnetlzation (no current and charges). If currents, charges and magnetization are present, then not even the knowledge of the divergences is a sufficient condition for such a determination. of Constant Mean Extrinsic Curvature. SIAN M. STUMBLES, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW England; and Center for Astrophysics, Harvard College Observatory and Smithsonian Astrophysical Observatory, Cambridge, Massachusetts 02138.

Hypersurfaces

The existence of hypersurfaces of constant mean extrinsic curvature is examined. Using techniques developed by Choquet-Bruhat in her work on related subjects and techniques used by D’Eath in his study of perturbed Robertson-Walker universes, theorems are proved about the existence of slices of constant mean extrinsic curvature for spacetimes in a neighbourhood of the open RobertsonWalker Universes. It is shown in particular that those spacetimes which lie in a neighbourhood of Minkowski space or de-Sitter space admit slices of constant mean extrinsic curvature. By modifying the techniques used to prove these theorems, it is shown that asymptotically simple spacetimes which are close to Minkowski space admit slices of constant mean extrinsic curvature. The behaviour of these slices near null infinity is examined and it is shown that a large family of such hypersurfaces exists, indexed by the BMS supertranslations. Behavior of Large N Fermionic Systems. DAVID A. KESSLER, Joseph Henry Laboratories, Princeton University, Princeton, New Jersey 08544; AND HERBERT LEVINE, Lyman Laboratory of Physics, Harvard University, Cambridge, Massachusetts 02138.

Classical

The large N limit of several fermionic systems in two dimensions is shown to be obtainable by doing classical mechanics. This generalizes results previously derived for bosonic models. For these types of theories, the reduction to a classical system of equations is closely related to the path integral quantization scheme of Dashen, Hasslacher and Neveu. Using this relationship, we are able to gain further insight into the workings of both approaches. A Systematic

Approach

AND A. PLASTINO. Argentina.

to the Hartree-Fock

Universidad

National,

Problem

Limit. G. GUTIERREZ de Ftsica, C. C. 67 (1900) La Plata,

in the Thermodynamic

Departamento

A systematic procedure is proposed in order to look for non-plane-wave solutions to the HartreeFock equations in the thermodynamic limit. The corresponding Hartree-Fock states are seen to

482 Copyright All rights

0 1981 by Academic Press, Inc. of reproduction in any form reserved.