Hamiltonian LGT in the complete Fourier analysis basis. The main problem in the Hamiltonian formulation of Lattice Gauge Theories is the determination of an appropriate basis avoiding the over-completeness arising from Mandelstam relations. We shortcut this problem using Harmonic analysis on Lie-Groups and intertwining operators formalism to explicitly construct a basis of the Hilbert space. Ou...

We study the possible singularities of isotropic cosmological models that have a varying speed of light as well as a varying gravitational constant. The field equations typically reduce to two dimensional systems which are then analyzed both by dynamical systems techniques in phase space and by applying the method of asymptotic splittings. In the general case we find initially expanding closed ...

We study the relation between center vortices and instantons in lattice QCD. One approach to understanding the physical origin of confinement and chiral symmetry breaking is to attempt to capture the essential physics in a much smaller number of degrees of freedom by projecting from a maximal abelian or maximal center gauge. For simplicity, we consider SU (2) and denote a link variable transfor...

Mean field theory has an unexpected group theoretic mathematical foundation. Instead of representation theory which applies to most group theoretic quantum models, Hartree-Fock and Hartree-Fock-Bogoliubov have been formulated in terms of coadjoint orbits for the groups U (n) and O(2n). The general theory of mean fields is formulated for any arbitrary Lie algebra g of fermion operators. The mome...

I give a quick summary of my proposal for simulating an improvement on quenched QCD with dynamical fermions which interact with the gluon configuration only via the topological index of the latter. It amounts to include only the topological part of the functional determinant into the measure, thereby absorbing a correction factor into the observable. I discuss the prospects of this concept from...

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In one of my first papers before the National Academy of Sciences' I showed by six drawings the operation of an Ionic Centrifuge in two types of discharge. The first three are shown correctly with negatively polarized end plates and insulated cylinder. The last three are shown incorrectly with the end plates voltage marked positive. But the current shown is due to the excess of positive ions ov...