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: Beyond the post Gaussian approximation
The post Gaussian effective potential in D=3 and D=2+2e are evaluated for the Ginzburg—Landau theory of superconductivity. It is shown that, the next order correction to the Gaussian approximation of the Ginzburg—Landau parameter κ is significant.This strongly indicates that strong correlations play dominant role in high T c superconductivity. In D=2+2e fractal dimensions Ginzburg Landau parameter turned out to be sensitive to e and the contribution of the post Gaussian term is larger than that for D = 3. Adjusting e to the recent experimental data on κ(T) for high — T c cuprate superconductor Tl 2 Ca 2 Ba 2 Cu 3 O 10(Tl − 2223), we find that e=0.21 is the best choice for this material. These results clearly show that, in order to understand high — T 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 the samples.
Finite-temperature generalized Gaussian effective potential
We evaluate the thermal corrections to the generalized Gaussian effective potential. We carry out the calculations of the lowest-order corrections in the case of self-interacting scalar fields in one and two spatial dimensions, and study the restoration of the symmetry at high temperatures.