Abstract:
Within the framework of the operator product expansion (OPE) and the renormalization group equation (RGE), we show that the temperature and chemical potential dependence of the zeroth moment of a spectral function (SF) in an asymptotically free theory is completely determined by the one-loop structure of the theory. This exact result constrains the qualitative shape of SF's, and implies striking phenomenological effects near phase transitions.

Abstract:
We generalize the concept of dimensional reduction to operators involving fermion fields in high temperature field theories. It is found that the ultraviolet behavior of the running coupling constant plays a crucial role. The general concept is illustrated explicitly in the Gross-Neveu model.

Abstract:
With SNO data on electron-neutrino flux from the sun, it is possible to derive the $\nu_e$ survival probability $P_{ee}(E)$ from existing experimental data of Super-Kamiokande, gallium experiments and Homestake. The combined data of SNO and Super-Kamiokande provide boron $\nu_e$ flux and the total flux of all active boron neutrinos, giving thus $P_{ee}(E)$ for boron neutrinos. The Homestake detector, after subtraction of the signal from boron neutrinos, gives the flux of Be+CNO neutrinos, and $P_{ee}$ for the corresponding energy interval, if the produced flux is taken from the Standard Solar Model (SSM). Gallium detectors, GALLEX, SAGE and GNO, detect additionally pp-neutrinos. The pp-flux can be calculated subtracting from the gallium signal the rate due to boron, beryllium and CNO neutrinos. The ratio of the measured $pp$-neutrino flux to that predicted by the SSM gives the survival probability for $pp$-neutrinos. Comparison with theoretical survival probabilities shows that the best (among known models) fit is given by LMA and LOW solutions.

Abstract:
Non-resonant fusion cross-sections significantly higher than corresponding theoretical predictions are observed in low-energy experiments with deuterated matrix target. Models based on thermal effects, electron screening, or quantum-effect dispersion relations have been proposed to explain these anomalous results: none of them appears to satisfactory reproduce the experiments. Velocity distributions are fundamental for the reaction rates and deviations from the Maxwellian limit could play a central role in explaining the enhancement. We examine two effects: an increase of the tail of the target Deuteron momentum distribution due to the Galitskii-Yakimets quantum uncertainty effect, which broadens the energy-momentum relation; and spatial fluctuations of the Debye-H\"{u}ckel radius leading to an effective increase of electron screening. Either effect leads to larger reaction rates especially large at energies below a few keV, reducing the discrepancy between observations and theoretical expectations.

Abstract:
By solving a differential-functional equation inposed by the MaxEnt principle we obtain a class of two-parameter deformed logarithms and construct the corresponding two-parameter generalized trace-form entropies. Generalized distributions follow from these generalized entropies in the same fashion as the Gaussian distribution follows from the Shannon entropy, which is a special limiting case of the family. We determine the region of parameters where the deformed logarithm conserves the most important properties of the logarithm, and show that important existing generalizations of the entropy are included as special cases in this two-parameter class.

Abstract:
A consistent generalization of statistical mechanics is obtained by applying the maximum entropy principle to a trace-form entropy and by requiring that physically motivated mathematical properties are preserved. The emerging differential-functional equation yields a two-parameter class of generalized logarithms, from which entropies and power-law distributions follow: these distributions could be relevant in many anomalous systems. Within the specified range of parameters, these entropies possess positivity, continuity, symmetry, expansibility, decisivity, maximality, concavity, and are Lesche stable. The Boltzmann-Shannon entropy and some one parameter generalized entropies already known belong to this class. These entropies and their distribution functions are compared, and the corresponding deformed algebras are discussed.

Abstract:
We discuss what appears the last hope for an astrophysical solution to the solar neutrino problem: a correlated variation of the astrophysical factors for the helium burning cross sections ($S_{33}$ and $S_{34}$) and either $S_{17}$ or the central temperature $T_c$. In this context, we recognize the important role played by the CNO neutrinos. In fact, we can obtain a fair fit to the experimental data only if three conditions are met simultaneously: the astrophysical factor $S_{33}$ is about 200 times what is presently estimated, the astrophysical factor $S_{17}$ is about 3 times larger and the $^{13}$N and $^{15}$O neutrino fluxes are negligible compared to the ones predicted by standard solar models. These conditions are not supported by the present data and their correlated combination is improbable.

Abstract:
We derive a lower limit on the Beryllium neutrino flux on earth, $\Phi(Be)_{min} = 1\cdot 10^9 cm^{-2} s^{-1}$, in the absence of oscillations, by using helioseismic data, the B-neutrino flux measured by Superkamiokande and the hydrogen abundance at the solar center predicted by Standard Solar Model (SSM) calculations. We emphasize that this abundance is the only result of SSMs needed for getting $\Phi(Be)_{min}$. We also derive lower bounds for the Gallium signal, $G_{min}=(91 \pm 3) $ SNU, and for the Chlorine signal, $C_{min}=(3.24\pm 0.14)$ SNU, which are about $3\sigma$ above their corresponding experimental values, $G_{exp}= (72\pm 6)$ SNU and $C_{exp}= (2.56\pm 0.22) $ SNU.

Abstract:
The excess of solar-neutrino events above 13 MeV that has been recently observed by Superkamiokande can be explained by the vacuum oscillation solution to the Solar Neutrino Problem (SNP). If the boron neutrino flux is 20% smaller than the standard solar model (SSM) prediction and the chlorine signal is assumed 30% (or 3.4 sigmas) higher than the measured one, there exists a vacuum oscillation solution to SNP that reproduces both the observed spectrum of the recoil electrons, including the high energy distortion, and the other measured neutrino rates. The most distinct signature of this solution is a semi-annual seasonal variation of the Be7 neutrino flux with maximal amplitude. While the temporal series of the GALLEX and Homestake signals suggest that such a seasonal variation could be present, future detectors (BOREXINO, LENS and probably GNO) will be able to test it.