A geometrical theory of spin motion

A discussion of the fundamental interrelation of geometry and physical laws with Lie groups leads to a reformulation and heuristic modification of the principle of inertia and the principle of equivalence, which is based on the simple de Sitter group instead of the Poincaré group. The resulting law of motion allows a unified formulation for structureless and spinning test particles. A metrical theory of gravitation is constructed with the modified principle, which is structured after the geometry of the manifold of the de Sitter group. The theory is equivalent to a particular Kaluza-Klein theory in ten dimensions with the Lorentz group as gauge group. A restricted version of this theory excludes torsion. It is shown by a reformulation of the energy momentum complex that this version is equivalent to general relativity with a cosmologic term quadratic in the curvature tensor and in which the existence of spinning particle fields is inherent from first principles. The equations of the general theory with torsion are presented and it is shown in a special case how the boundary conditions for the torsion degree of freedom have to be chosen such as to treat orbital and spin angular momenta on an equal footing. The possibility of verification of the resulting anomalous spin-spin interaction is mentioned and a model imposed by the group topology ofSO(3,2) is outlined in which the unexplained discrepancy between the magnitude of the discrete valued coupling constants and the gravitational constant in Kaluza-Klein theories is resolved by the identification of identical fermions as one orbit. The mathematical structure can be adapted to larger groups to include other degrees of freedom.     

Asymptotic chaos

We provide in table I a list of normal forms of ordinary differential equations describing the dynamics of physical systems in conditions near to the simultaneous onset of up three instabilities. The first (quadratic) terms in the Taylor series for the nonlinear terms in these amplitude equations (as they are called in fluid dynamics) are given in each case. We focus on a particular example involving three instabilities and derive an asymptotic version of the corresponding normal form as a limit of small dissipation is approached. The numerical investigation of this asymptotic normal form strongly suggests that chaotic behavior occurs as close as one wants to the onset of the triple instability. This chaotic behavior is also exhibited by a return map constructed by direct numerical experiments on the amplitude equation. We also derive by analytic methods a model return map that qualitatively reproduces much of the dynamics observed numerically in the solutions of the asymptotic normal form in nearly homoclinic conditions. In the limit of strong contraction, this model map of the plane reduces to a unidimensional map that is valuable in understanding the dynamics of the original system.     

Equivalence of the degrees of freedom in a unified gravitational theory

A discussion of the nouniqueness of physical laws and their invariance groups is illustrated by the construction of a physical theory (presented earlier) in which the law of motion of structureless and spinning particles is unified in the geometry of the manifold of the de Sitter groupSO(3,2). The theory has the structure of a non-Abelian Kaluza-Klein theory with very special properties resulting from the topology and noncompactness of the groups. The physical interpretation of the field equation is discussed. The physical requirement of equivalence of the interaction of spinning and orbiting systems, generally unconsidered in related theories, is here taken into account by the structure of the theory. The possibility of deviations from predictions of general relativity exists. Generalizations of the theoretical structure to higher dimensional groups are outlined and open the possibility for observations.     

Methylierungsversuche an Stärke

Ohne Zusammenfassung     

Über reelle Primzahlen

Ohne Zusammenfassung     

The neutral weak current in muonic atoms

The measurement of parity-odd observables in muonic atoms has eluded realization for ten years. Nevertheless, determination of the coupling constants which characterize the weak neutral current of muons remains an important goal. Since the muonic atom is essentially an hydrogen-like system, the precise determination of neutral current couplings and observation of higher order weak and electromagnetic corrections may be possible. Moreover, the effects of neutral currents in atomic systems are determined by a different combination of couplings than effects measured at high energy. Finally, comparison of effects in muonic and conventional atoms would confirm the university of neutral current couplings.Current proposals to measure parity-odd observables exploit the physics of nuclei and atoms as well as of muonic atoms. This report attempts a systematic presentation of the physics required to understand the proposals and the interpretation of the measurements. The three most promising measurements in thulium, neon and boron are discussed in detail.     

Über die Exponentialfunction

Ohne Zusammenfassung     

Autologous fat implantation for vocal fold scar: A preliminary report

New insights into the anatomy and physiology of phonation, along with technological advances in voice assessment and quantification, have led to dramatic improvements in medical voice care. Techniques to prevent vocal fold scar have been among the most important, especially scarring and hoarseness associated with voice surgery. Nevertheless, dysphonia due to vocal fold scar is still encountered all too frequently. Although it is not generally possible to restore such injured voices to normal, patients with scar-induced dysphonia can usually be helped. Voice improvement is optimized through a team approach. Treatment may include sophisticated voice therapy and vocal fold surgery. Although experience with collagen injection has been encouraging in selected cases (particularly in those involving limited areas of vocal fold scar), there is no consistently successful surgical technique. Attempts to treat massive vocal fold scar, such as may be seen following vocal fold stripping, have been particularly unsuccessful. This paper reports preliminary experience with the implantation of autologous fat into the vibratory margin of the vocal fold of patients with severe, extensive scarring. Using this technique, it appears possible to recreate a mucosal wave and improve voice quality. Additional research is needed.