Abstract:
In the past, the phase-space elementary cell of a non-quantized system was set equal to the third power of the Planck constant; in fact, it is not a necessary assumption. We discuss how the phase space volume, the number of states and the elementary-cell volume of a system of non-interacting N particles, changes when an interaction is switched on and the system becomes or evolves to a system of correlated non-Boltzmann particles and derives the appropriate expressions. Even if we assume that nowadays the volume of the elementary cell is equal to the cube of the Planck constant, h3, at least for quantum systems, we show that there is a correspondence between different values of h in the past, with important and, in principle, measurable cosmological and astrophysical consequences, and systems with an effective smaller (or even larger) phase-space volume described by non-extensive generalized statistics.

Abstract:
We discuss the interpretation of Euclidean correlation functions at finite temperature ($T$) and their relationship with the corresponding real-time Green's functions. The soluble 2+1 dimensional Gross-Neveu model in the large-$N$ limit is used throughout as a working example. First, the real-time bound state, identified as an elementary excitation at finite $T$, is solved. The bound state mass, the dispersion relation at low momenta, the coupling constant and decay constant are calculated. To characterize the structure of the bound state the on-shell form factor is carefully introduced and calculated. Then we examine the corresponding screening state and contrast the screening mass, coupling constant, decay constant and the screening Bethe-Salpeter amplitude with the real-time quantities. We find that, although they can be used as qualitative indicators in the low-$T$ regime, the screening states at finite $T$ in general do not reflect the properties of the corresponding real-time bound states. Besides, other relevant issues, such as the subtlety of the real-time manifestation of conservation laws due to some internal symmetries at $T\ne 0$, the temperature dependence of the pseudoscalar spectral function and its sum rule, and the high-$T$ limit of the screening state and its implications to the dimensional reduction, are also discussed in detail.

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) is completely determined by the one-loop structure in an asymptotically free theory, and in particular in QCD. Logarithmic corrections are found to play an essential role in the derivation. This exact result constrains the shape of SF's, and implies striking effects near phase transitions. Phenomenological parameterizations of the SF, often used in applications such as the analysis of lattice QCD data or QCD sum rule calculations at finite temperature and baryon density must satisfy these constraints. We also explicitly illustrate in detail the exact sum rule in the Gross-Neveu model.

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) is completely determined by the one-loop structure of an asymptotically free theory. This exact result constrains the shape of SF's, and implies a highly non-trivial functional form for the SF near second order, or weak first order, phase transitions. Phenomenological parameterizations of the SF, often used in applications such as the analysis of lattice QCD data or QCD sum rule calculations at finite temperature and baryon density, must satisfy these constraints.

Abstract:
We introduce the running coupling constant of QCD in the high temperature phase, $\tilde{g}^2(T)$, through a renormalization scheme where the dimensional reduction is optimal at the one-loop level. We then calculate the relevant scale parameter, $\Lambda_T$, which characterizes the running of $\tilde{g}^2(T)$ with $T$, using the background field method in the static sector. It is found that $\Lambda_T/\Lambda_{\overline{\text{MS}}} =e^{(\gamma_E+1/22)}/(4\pi)\approx 0.148$. We further verify that the coupling $\tilde{g}^2(T)$ is also optimal for lattice perturbative calculations. Our result naturally explains why the high temperature limit of QCD sets in at temperatures as low as a few times the critical temperature. In addition, our $\Lambda_T$ agrees remarkably well with the scale parameter determined from the lattice measurement of the spatial string tension of the SU(2) gauge theory at high $T$.

Abstract:
We performed two independent counting experiments on a beta-emitting source of Sm151 by measuring the gamma-photon emitted in a fraction of the decays. For counting times ranging from 10**-3 to 5.12*10**4 seconds, our measurements show no evidence of deviations from Poissonian behavior and, in particular, no sign of 1/f noise. These measurements put strong limits on non-Poissonian components of the fluctuations for the subset of decays accompanied by gamma, and corresponding limits for the total number of beta-decays. In particular, the magnitude of a hypothetical flicker floor is strongly bounded also for the beta-decay. This result further constrains theories predicting anomalous fluctuations in nuclear decays.

Abstract:
The concept of dimensional reduction in the high temperature regime is generalized to static Green's functions of composite operators that contain fermionic fields. The recognition of a natural kinematic region where the lowest Matsubara modes are close to their mass-shell, and the ultraviolet behavior of the running coupling constant of the original theory are crucial for providing the necessary scale hierarchy. The general strategy is illustrated in the asymptotically-free Gross-Neveu model in 1+1 dimensions, where we verify that dimensional reduction occurs to the leading order in $g^2(T)$. We also find, in the same model, that the scale parameter characterizing the dependence on temperature of the coupling constant in the reduced theory, $\Lambda_T$, is considerably smaller than $\Lambda_{\bar{\text{MS}}}$. Implications of our results for QCD are also discussed.

Abstract:
We show that QCD undergoes dimensional reduction at high temperatures also in the quark sector. In the kinematic region relevant to screening physics, where the lowest Matsubara modes are close to their ``mass-shells'', all static Green's functions involving both quarks and gluons, are reproducible in the high-$T$ limit by a renormalizable three dimensional Lagrangian up to order $\tilde{g}^2(T)\sim 1/ln T$. This three dimensional theory only contains explicitly the lightest bosonic and fermionic Matsubara modes, while the heavier modes correct the tree-level couplings and generate extra local vertices. We also find that the quark degrees of freedom that have been retained in the reduced theory are nonrelativistic in the high-$T$ limit. We then improve our result to order $\tilde{g}^4(T)$ through an explicit nonrelativistic expansion, in the spirit of the heavy quark effective theory. This effective theory is relevant for studying QCD screening phenomena with observables made from quarks, e.g. mesonic and baryonic currents, already at temperatures not much higher than the chiral transition temperature $T_c$.

Abstract:
This article illustrates how very small deviations from the Maxwellian exponential tail, while leaving unchanged bulk quantities, can yield dramatic effects on fusion reaction rates and discuss several mechanisms that can cause such deviations.

Abstract:
The deepest hole that has ever been dug is about 12 km deep. Geochemists analyze samples from the Earth's crust and from the top of the mantle. Seismology can reconstruct the density profile throughout all Earth, but not its composition. In this respect, our planet is mainly unexplored. Geo-neutrinos, the antineutrinos from the progenies of U, Th and K40 decays in the Earth, bring to the surface information from the whole planet, concerning its content of natural radioactive elements. Their detection can shed light on the sources of the terrestrial heat flow, on the present composition, and on the origins of the Earth. Geo-neutrinos represent a new probe of our planet, which can be exploited as a consequence of two fundamental advances that occurred in the last few years: the development of extremely low background neutrino detectors and the progress on understanding neutrino propagation. We review the status and the prospects of the field.