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Remarks on a class of almost trivial solutions of the gravitational field equation
ANNALS
OF PHYSICS:
49, 540 (1968)
Abstracts
of Papers
to Appear
in Future
Issues
Radiative Corrections to Pion-Nucleon Coupling Constants. LUTHER KENT MORRISON. Department of Physics, Brandeis University, Waltham, Massachusetts. The electromagnetic corrections to the n-N coupling constants have been calculated by four methods. Feynman graphs, sidewise dispersion relations, sum rules, and current commutation relations. The results are explicitly shown to be gauge invariant. Only the nucleon intermediate state is considered in the Feynman approach and the dispersion relation approach, but the effect of the N* (1238) intermediate state is estimated in the commutation relation approach. The elastic electromagnetic form factors are used to cut off the integrals for the Feynman graphs and sum rules, and an ultraviolet cutoff is used in the dispersion integrals. The uses of PCAC and quark model current-current commutators for calculating the coupling constant shifts are shown to be model dependent and to lead to a logarithmic divergence. Comparisons of the various methods are made; although numerical results do not agree, they are generally in the direction required to understand charge dependent effects in N-N scattering. Pole Approximation in Potential Scattering. H. MORAWITZ. IBM Research Laboratory, Monterey and Cottle Roads, San Jose, California. A simple approximation for calculating S-wave scattering in potential theory at certain discrete energies E(a) = (I$~, H&), with d=(r) a suitable function vanishing as r --f co, is proposed. It corresponds to replacing the right-hand branchcut in the scattering amplitude due to unitarity by a simple pole at E = E(a) and places scattering on the same footing as the bound-state problem. Numerical results for the attractive exponential and Yukawa potential are given. Gravitation Without Self-interaction. S. DESER AND B. E. LAURENT. Department of Physics, Brandeis University, Waltham, Massachusetts. We explore the possibility that the gravitational field is a linear spin-two field. As is well-known such a field must have a divergence-free source. But when matter interacts with the gravitational held, its stress tensor is not divergence-free and therefore cannot serve as the source. Instead, we have chosen a divergence-free, nonlocal, projection of the matter stress tensor. It is shown that it gives the same predictions as general relativity in all experimental and observational tests made so far; it is in fact difficult to decide, experimentally, between the two theories. Conceptually there are basic differences. The principle of equivalence is fulfilled for matter but not for gravitons, which are “uncharged,” like photons in electrodynamics. There are indications that gravitational collapse does not occur. The theory may be written in local form, using auxiliary fields; these correspond to an additional spin-zero excitation (with positive definite energy). Remarks on a Class of’ Almost Trivial Solutions of the Gravitational Field Equation. K. KRAUS. Institute for Theoretical Physics Universitlt Marburg, Marburg, Germany. A new class of static solutions of Einstein’s vacuum field equation ReL = 0 is described. The solutions are locally flat, but possess line singularities and global space curvature. Being analogous to the electromagnetic field of an infinitely long and infinitely thin solenoid, they give rise to gravitational analogues of the Aharonov-Bohm effect. Furthermore, they provide examples for a conjecture on asymptotic global flatness.
540
OF PHYSICS:
49, 540 (1968)
Abstracts
of Papers
to Appear
in Future
Issues
Radiative Corrections to Pion-Nucleon Coupling Constants. LUTHER KENT MORRISON. Department of Physics, Brandeis University, Waltham, Massachusetts. The electromagnetic corrections to the n-N coupling constants have been calculated by four methods. Feynman graphs, sidewise dispersion relations, sum rules, and current commutation relations. The results are explicitly shown to be gauge invariant. Only the nucleon intermediate state is considered in the Feynman approach and the dispersion relation approach, but the effect of the N* (1238) intermediate state is estimated in the commutation relation approach. The elastic electromagnetic form factors are used to cut off the integrals for the Feynman graphs and sum rules, and an ultraviolet cutoff is used in the dispersion integrals. The uses of PCAC and quark model current-current commutators for calculating the coupling constant shifts are shown to be model dependent and to lead to a logarithmic divergence. Comparisons of the various methods are made; although numerical results do not agree, they are generally in the direction required to understand charge dependent effects in N-N scattering. Pole Approximation in Potential Scattering. H. MORAWITZ. IBM Research Laboratory, Monterey and Cottle Roads, San Jose, California. A simple approximation for calculating S-wave scattering in potential theory at certain discrete energies E(a) = (I$~, H&), with d=(r) a suitable function vanishing as r --f co, is proposed. It corresponds to replacing the right-hand branchcut in the scattering amplitude due to unitarity by a simple pole at E = E(a) and places scattering on the same footing as the bound-state problem. Numerical results for the attractive exponential and Yukawa potential are given. Gravitation Without Self-interaction. S. DESER AND B. E. LAURENT. Department of Physics, Brandeis University, Waltham, Massachusetts. We explore the possibility that the gravitational field is a linear spin-two field. As is well-known such a field must have a divergence-free source. But when matter interacts with the gravitational held, its stress tensor is not divergence-free and therefore cannot serve as the source. Instead, we have chosen a divergence-free, nonlocal, projection of the matter stress tensor. It is shown that it gives the same predictions as general relativity in all experimental and observational tests made so far; it is in fact difficult to decide, experimentally, between the two theories. Conceptually there are basic differences. The principle of equivalence is fulfilled for matter but not for gravitons, which are “uncharged,” like photons in electrodynamics. There are indications that gravitational collapse does not occur. The theory may be written in local form, using auxiliary fields; these correspond to an additional spin-zero excitation (with positive definite energy). Remarks on a Class of’ Almost Trivial Solutions of the Gravitational Field Equation. K. KRAUS. Institute for Theoretical Physics Universitlt Marburg, Marburg, Germany. A new class of static solutions of Einstein’s vacuum field equation ReL = 0 is described. The solutions are locally flat, but possess line singularities and global space curvature. Being analogous to the electromagnetic field of an infinitely long and infinitely thin solenoid, they give rise to gravitational analogues of the Aharonov-Bohm effect. Furthermore, they provide examples for a conjecture on asymptotic global flatness.
540