Irreducible Representations of an Algebra underlying Hidden Symmetries of a class of Quasi Exactly Solvable Systems of Equations

The set of linear, differential operators preserving the vector space of couples of polynomials of degrees n and n-2 in one real variable leads to an abstract associative graded algebra A(2). The irreducible, finite dimensional representations of this algebra are classified into five infinite discrete sets and one exceptional case. Their matrix elements are given explicitely. The results are related to the theory of quasi exactly solvable equations.Comment: 38 pages, late

Yang-Mills theory for non-semisimple groups

For semisimple groups, possibly multiplied by U(1)'s, the number of Yang-Mills gauge fields is equal to the number of generators of the group. In this paper, it is shown that, for non-semisimple groups, the number of Yang-Mills fields can be larger. These additional Yang-Mills fields are not irrelevant because they appear in the gauge transformations of the original Yang-Mills fields. Such non-semisimple Yang-Mills theories may lead to physical consequences worth studying. The non-semisimple group with only two generators that do not commute is studied in detail.Comment: 16 pages, no figures, prepared with ReVTeX

Beam Energy Considerations for Gold Nano-Particle Enhanced Radiation Treatment

Purpose: A novel approach using nano technology enhanced radiation modalities is investigated. The proposed methodology uses antibodies labeled with organically inert metals with a high atomic number. Irradiation using photons with energies in the kilo--electron volt (keV) range show an increase in dose due to a combination of an increase in photo-electric interactions and a pronounced generation of Auger and/or Coster-Kronig (A-CK) electrons. Methods: The dependency of the dose deposition on various factors is investigated using Monte Carlo simulation models. The factors investigated include: agent concentration, spectral dependency looking at mono--energetic sources as well as classical bremsstrahlung sources. The optimization of the energy spectrum is performed in terms of physical dose enhancement as well as the dose deposited by Auger and/or Coster-Kronig electrons and their biological effectiveness. Results: A quasi-linear dependency on concentration and an exponential decrease within the target medium is observed. The maximal dose enhancement is dependent on the position of the target in the beam. Apart from irradiation with low photon energies (10 - 20 keV) there is no added benefit from the increase in generation of Auger electrons. Interestingly, a regular 110kVp bremsstrahlung spectrum shows a comparable enhancement in comparison with the optimized mono--energetic sources. Conclusions: In conclusion we find that the use of nano-particle enhanced shows promise to be implemented quite easily in regular clinic on a physical level due to the advantageous properties in classical beams.Comment: Preprint submitted to Phys Med Bio

Democratic Supersymmetry

We present generalisations of N-extended supersymmetry algebras in four dimensions, using Lorentz covariance and invariance under permutation of the N supercharges as selection criteria.Comment: 26 pages, latex fil

Kaluza-Klein towers for real vector fields in flat space

We consider a free real vector field propagating in a five dimensional flat space with its fifth dimension compactified either on a strip or on a circle and perform a Kalaza Klein reduction which breaks SO(4,1) invariance while reserving SO(3,1) invariance. Taking into account the Lorenz gauge condition, we obtain from the most general hermiticity conditions for the relevant operators all the allowed boundary conditions which have to be imposed on the fields in the extra-dimension. The physical Kaluza-Klein mass towers, which result in a four-dimensional brane, are determined in the different distinct allowed cases. They depend on the bulk mass, on the parameters of the boundary conditions and on the extra parameter present in the Lagrangian. In general, they involve vector states together with accompanying scalar states.Comment: 28 pages, 4 independent table