In a recent letter, the AMS collaboration reported the detailed and extensive data concerning the distribution in energy of electron and positron cosmic rays. A central result of the experimental work resides in the energy regime $30 {rm GeV}< E < 1
{rm TeV}$ wherein the power law exponent of the energy distribution is measured to be $alpha ({rm experiment})=3.17$. In virtue of the Fermi statistics obeyed by electrons and positrons, a theoretical value was predicted as $alpha ({rm theory})=3.151374$ in very good agreement with experimental data. The consequences of this agreement between theory and experiment concerning the sources of cosmic ray electrons and positrons are briefly explored.
We have recently shown that the cosmic ray energy distributions as detected on earthbound, low flying balloon or high flying satellite detectors can be computed by employing the heats of evaporation of high energy particles from astrophysical sources
. In this manner, the experimentally well known power law exponents of the cosmic ray energy distribution have been theoretically computed as 2.701178 for the case of ideal Bose statistics, 3.000000 for the case of ideal Boltzmann statistics and 3.151374 for the case of ideal Fermi statistics. By ideal we mean virtually zero mass (i.e. ultra-relativistic) and noninteracting. These results are in excellent agreement with the experimental indices of 2.7 with a shift to 3.1 at the high energy ~ PeV knee in the energy distribution. Our purpose here is to discuss the nature of cosmic ray power law exponents obtained by employing conventional thermal quantum field theoretical models such as quantum chromodynamics to the cosmic ray sources in a thermodynamic scheme wherein gamma and zeta function regulation is employed. The key reason for the surprising accuracy of the ideal boson and ideal fermion cases resides in the asymptotic freedom or equivalently the Feynman parton structure of the ultra-high energy tails of spectral functions.
There is a recent comment (Ciuchi et al., 2012) concerning the theory of collective many body effects on the neutron production rates in a chemical battery cathode. Ciuchi et al employ an inverse beta decay expression that contains a two body amplitu
de. Only one electron and one proton may exist in the Ciuchi et al model initial state wave function. A flaw in their reasoning is that one cannot in reality describe collective many body correlations with only a two particle wave function. One needs very many particles to describe collective effects. In the model wave functions of Ciuchi et al there are no metallic hydrides, there are no cathodes and there are no chemical batteries. Employing a wave function with only one electron and one proton is inadequate for describing collective metallic hydride surface quantum plasma physics in cathodes accurately.
Recent experimental reports of super-luminal velocity neutrinos moving between Geneva and Gran Sasso in no way contradict the special relativity considerations of conventional quantum field theory. A neutrino exchanged between Geneva and Gran Sasso i
s both virtual and space-like. The Lorentz invariant space-like distance $L$ and the Lorentz invariant space-like four momentum transfered $varpi $ between Geneva and Gran Sasso can be extracted from experimental data as will be shown in this work.
The standard model of strong interactions invokes the quantum chromodynamics (QCD) of quarks and gluons interacting within a fluid. At sufficiently small length scales, the effective interactions between the color charged particles within the fluid a
re thought to be weak. Short distance asymptotic freedom provides the perturbation theory basis for comparisons between QCD theory and laboratory high energy scattering experiments. It is here shown that the asymptotically free vacuum has negative dissipation implicit in the color electrical conductivity. Negative dissipation implies an asymptotically free QCD negative temperature {em excited state amplifier} unstable to decay. The qualitative experimental implications of this instability are explored.
