Partial and Quasi Dynamical Symmetries in Nuclei

One of the interesting aspects in the study of atomic nuclei is the strikingly regular behaviour many display in spite of being complex quantum-mechanical systems, prompting the universal question of how regularity emerges out of complexity. It is often conjectured that symmetries play a pivotal role in our understanding of this emerging simplicity. But most symmetries are likely to be broken, partial or both. Under such more realistic conditions, does the concept of symmetry still provide a basis for our understanding of regularity? I suggest that this requires the enlarged concepts of partial and quasi dynamical symmetry.Comment: 5 pages, 5 figures, accepted for publication in Nuclear Physics New

Neutron-proton pairs in nuclei

A review is given of attempts to describe nuclear properties in terms of neutron--proton pairs that are subsequently replaced by bosons. Some of the standard approaches with low-spin pairs are recalled but the emphasis is on a recently proposed framework with pairs of neutrons and protons with aligned angular momentum. The analysis is carried out for general $j$ and applied to $N=Z$ nuclei in the $1f_{7/2}$ and $1g_{9/2}$ shells.Comment: 16 figures, 4 tables, accepted for publication in Int. J. of Modern Physics

Seniority in quantum many-body systems

The use of the seniority quantum number in many-body systems is reviewed. A brief summary is given of its introduction by Racah in the context of atomic spectroscopy. Several extensions of Racah's original idea are discussed: seniority for identical nucleons in a single-$j$ shell, its extension to the case of many, non-degenerate $j$ shells and to systems with neutrons and protons. To illustrate its usefulness to this day, a recent application of seniority is presented in Bose--Einstein condensates of atoms with spin.Comment: 16 pages, 1 figure, accepted for publication in the Proceedings of The American Institute of Physic

Harmonic Superspaces from Superstrings

We derive harmonic superspaces for N=2,3,4 SYM theory in four dimensions from superstring theory. The pure spinors in ten dimensions are dimensionally reduced and yield the harmonic coordinates. Two anticommuting BRST charges implement Grassmann analyticity and harmonic analyticity. The string field theory action produces the action and field equations for N=3 SYM theory in harmonic superspace.Comment: 14 pp. Harvma

Absolute Time Derivatives

A four dimensional treatment of nonrelativistic space-time gives a natural frame to deal with objective time derivatives. In this framework some well known objective time derivatives of continuum mechanics appear as Lie-derivatives. Their coordinatized forms depends on the tensorial properties of the relevant physical quantities. We calculate the particular forms of objective time derivatives for scalars, vectors, covectors and different second order tensors from the point of view of a rotating observer. The relation of substantial, material and objective time derivatives is treated.Comment: 26 pages, 4 figures (minor revision