Yang-Mills Fields Quantization in the Factor Space

The perturbation theory over inverse interaction constant $1/g$ is constructed for Yang-Mills theory. It is shown that the new perturbation theory is free from the gauge ghosts and Gribov's ambiguities, each order over $1/g$ presents the gauge-invariant quantity. It is remarkable that offered perturbation theory did not contain divergences, at least in the vector fields sector, and no renormalization procedure is necessary for it.Comment: 27 pages, Latex, no figure

Functional PCA for Remotely Sensed Lake Surface Water Temperature Data

Functional principal component analysis is used to investigate a high-dimensional surface water temperature data set of Lake Victoria, which has been produced in the ARC-Lake project. Two different perspectives are adopted in the analysis: modelling temperature curves (univariate functions) and temperature surfaces (bivariate functions). The latter proves to be a better approach in the sense of both dimension reduction and pattern detection. Computational details and some results from an application to Lake Victoria data are presented

Effective Field Theory Approach to High-Temperature Thermodynamics

An effective field theory approach is developed for calculating the thermodynamic properties of a field theory at high temperature $T$ and weak coupling $g$. The effective theory is the 3-dimensional field theory obtained by dimensional reduction to the bosonic zero-frequency modes. The parameters of the effective theory can be calculated as perturbation series in the running coupling constant $g^2(T)$. The free energy is separated into the contributions from the momentum scales $T$ and $gT$, respectively. The first term can be written as a perturbation series in $g^2(T)$. If all forces are screened at the scale $gT$, the second term can be calculated as a perturbation series in $g(T)$ beginning at order $g^3$. The parameters of the effective theory satisfy renormalization group equations that can be used to sum up leading logarithms of $T/(gT)$. We apply this method to a massless scalar field with a $\Phi^4$ interaction, calculating the free energy to order $g^6 \log g$ and the screening mass to order $g^5 \log g$.Comment: 40 pages, LaTeX, 5 uuecoded figure

Renormalization Group Functions of the \phi^4 Theory in the Strong Coupling Limit: Analytical Results

The previous attempts of reconstructing the Gell-Mann-Low function \beta(g) of the \phi^4 theory by summing perturbation series give the asymptotic behavior \beta(g) = \beta_\infty g^\alpha in the limit g\to \infty, where \alpha \approx 1 for the space dimensions d = 2,3,4. It can be hypothesized that the asymptotic behavior is \beta(g) ~ g for all values of d. The consideration of the zero-dimensional case supports this hypothesis and reveals the mechanism of its appearance: it is associated with a zero of one of the functional integrals. The generalization of the analysis confirms the asymptotic behavior \beta(g)=\beta_\infty g in the general d-dimensional case. The asymptotic behavior of other renormalization group functions is constant. The connection with the zero-charge problem and triviality of the \phi^4 theory is discussed.Comment: PDF, 17 page