Paul Adrien Maurice Dirac (1902–1984)

Foundations of Physics -     

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.     

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.     

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.     

Nature-inspired dimerization as a strategy to modulate neuropeptide pharmacology exemplified with vasopressin and oxytocin

Vasopressin (VP) and oxytocin (OT) are cyclic neuropeptides that regulate fundamental physiological functions via four G protein-coupled receptors, V_1aR, V_1bR, V₂R, and OTR. Ligand development remains challenging for these receptors due to complex structure–activity relationships. Here, we investigated dimerization as a strategy for developing ligands with novel pharmacology. We regioselectively synthesised and systematically studied parallel, antiparallel and N- to C-terminal cyclized homo- and heterodimer constructs of VP, OT and dVDAVP (1-deamino-4-valine-8-d-arginine-VP). All disulfide-linked dimers, except for the head-to-tail cyclized constructs, retained nanomolar potency despite the structural implications of dimerization. Our results support a single chain interaction for receptor activation. Dimer orientation had little impact on activity, except for the dVDAVP homodimers, where an antagonist to agonist switch was observed at the V_1aR. This study provides novel insights into the structural requirements of VP/OT receptor activation and spotlights dimerization as a strategy to modulate pharmacology, a concept also frequently observed in nature.

Structural and pharmacological study of parallel, antiparallel and N- to C-terminal cyclized homo- and heterodimers of vasopressin and oxytocin. This study spotlights dimerization as a strategy to modulate the pharmacology of neuropeptides.     

Optimization and validation of arsenic determination in foods by hydride generation flame atomic absorption spectrometry

A hydride generation flame atomic absorption spectrometric method was developed and optimized to quantitate arsenic (As) in foods. A wet digestion of the samples with HNO3 + H2O2 was performed and excess oxidants were eliminated by addition of hydrochloric acid and urea. As5+ in As3+ was then reduced by potassium iodide. The As3+ solution was analyzed by generation of arsine with sodium tetrahydroborate. As determination ranged from 2.5 to 20 microg/L, with a determination coefficient of 0.997. The limits of detection (LOD) and quantitation (LOQ) were 0.6 and 2.1 microg/L, respectively. The method was validated and good results were obtained for recovery, precision, accuracy, LOD, and LOQ. This method is now used to analyze foods from Rwanda.     

Characterization and examples of Chen submanifolds

In terms of an operator of J. Simons we give a new characterization for the Chen submanifolds orA-submanifolds of Riemannian manifolds. Also we give a number of non-trivial examples of Chen surfaces and study the impact of a conformal change of the metric of the ambient space on the property of being anA-surface.