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Electronics corresponds to the movement of electrons. These are manipulated by forces which act on these electrons by virtue of its elementary charge /e. An electron, in addition to its charge, carries a small magnetic moment ?, the principal origin of magnetism in the 3d transition series. Exploited in spin electronics are the forces acting on the moment ? and the associated current of angular momentum. Most non-volatile memory, e.g., a hard drive, involves reversing magnetic domains of magnetic materials. Through these forces and currents, spin electronics makes possible, e.g., hard drives with no moving parts.Part of the research proposed has to do with a circuit theory for spin electronics. The construction of such a circuit theory requires a better understanding of the microscopic theory of magnetism. Typically, e.g., Ni is considered as an itinerant ferromagnet, which would be described by the Stoner model. However the observation of spin waves in, e.g., Ni, implies the existence of localised moments and which this model does not describe. There exist modern methods involving quantum field theories, the concept of a Berry phase, and so called slave bosons, which can be used to address these questions. This is an important part of the research proposed here. The realisation of room temperature superconductivity would have many important applications. In part, the development of room temperature superconductors is inhibited by the lack of an adequate theoretical understanding. In the context of current high temperature superconductors, that anti-ferromagnetism and superconductivity are related is embodied in the SO(5) theory due to S. C. Zhang. This connects standard BCS superconductivity with anti-ferromagnetism. On the other hand P. W. Anderson has proposed an alternative RVB theory for the superconductivity in the high temperature superconductors. Models are often formulated using the slave boson method. This method effectively splits an electron into a holon, which carries a charge e but no magnetic moment and a spinon, which carries the magnetic moment ?. The holon is a boson while the spinon is a fermion. Mathematically this method is difficult because of a requirement that a charge Qi = 1. It is proposed here to actually exploit this to define a unit sphere. Rotations on the unit sphere Qi = 1 mix these bosons and fermions reflecting a super-symmetry. In the resulting SU(3) theory, rotations mix now RVB superconductivity and anti-ferromagnetism and will lead to different predictions with respect to experiment.The Kondo effect was originally an obscure effect, which occurred at very low temperatures in certain noble metals, which contained very small amounts of magnetic impurities. It was a difficult mathematical problem that turned out to have many rather strange properties depending upon the details of the model involved. Again in the context of spin electronics and in connection with quantum dots, etc., which might find application for quantum computation, this has again become a problem of importance. The existing theoretical methods are rather special and cannot be readily be adapted to the new situations encountered in experiment. The renormalisation group approach can be applied to this problem either numerically or approximately as was done in the past with considerable success. Such approaches use methods borrowed from elementary particle theory where, e.g., the charge of the electron is renormalized, i.e., treat is the coupling constant, as the object of study. The result is a first order differential equation. Another approach studies a mass, the effective magnetic field, and leads, to a second order differential equation. This approach is reproduces most known exact results for the Kondo problem. It is proposed to put this approach in a more modern form and apply it to the more complicated problems of interest in the above context.
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