Optimized post Gaussian approximation in the background field method
We have extended the variational perturbative theory based on the back ground field method to include the optimized expansion of Okopinska and the post Gaussian effective potential of Stansu and Stevenson. This new method provides much simpler way to compute the correction terms to the Gausssian effective action (or potential). We have also renormalized the effective potential in 3+1 dimensions by introducing appropriate counter terms in the lagrangian
Ginzburg-Landau theory of superconductivity at fractal dimensions
The post-Gaussian effective potential in D=2+2{epsilon} dimensions is evaluated for the Ginzburg-Landau theory of superconductivity. Two- and three-loop integrals for the post-Gaussian correction terms in D=2+2{epsilon} dimensions are calculated and {epsilon} expansions for these integrals are constructed. In D=2+2{epsilon} fractal dimensions the Ginzburg-Landau parameter turned out to be sensitive to {epsilon} and the contribution of the post-Gaussian term is larger than that for D=3. Adjusting {epsilon} to the recent experimental data on {kappa}(T) for the high-T{sub c} cuprate superconductor Tl{sub 2}Ca{sub 2}Ba{sub 2}Cu{sub 3}O{sub 10}, we found that {epsilon}=0.21 is the best choice for this material. The result clearly shows that, in order to understand high-T{sub c} superconductivity, it is necessary to include the fluctuation contribution as well as the contribution from the dimensionality of the sample. The method gives a theoretical tool to estimate the effective dimensionality of samples.
The unfolded universe of elementary particles. A geometric explanation of the standard model structure
We propose a geometric explanation of the standard model of Glashow, Weinberg and Salam for the known elementary particles. Our model is a generic Quantum Field Theory in dimension four, obtained by developing along a Lorentz sub-manifold the lagrangian of Einstein and Dirac in dimension twelve. The main mechanism which gives birth to the standard model is a certain gauge fixing of triality, which permits to identify the multiplicity of fermions, as seen from the four dimensional world, with the eight unseen dimensions of the generating universe. In this way we get the known tables of particles, explaining the series of fermions and the gauge bosons. We suggest that the Higgs field dynamics could appear through a bosonization of the right handed neutrino and correspond to a displacement in the unseen dimensions. We also propose hypotheses for dark matter, and perhaps dark energy. Then we suggest predictions to go beyond the standard model.