Relic Neutrinos: a Relativistic Mean Field Theory for the Free Fermi Gas

by Dr Bob McElrath

Tuesday Oct 18, 2011, 3:30 PM → 4:30 PM Pacific/Honolulu

112 (Watanabe Hall)

Relic neutrinos and dark matter present serious experimental difficulties in measuring their properties, and even proving their existence in the laboratory. If we are lucky the LHC and direct detection will tell us about dark matter, but one should not plan on luck, and we still know nothing about relic neutrinos. A completely unexplored avenue is that there could exist collective excitations of a quantum nature in these media that may be experimentally accessible. First we will show the relevant approximation necessary to create an effective field theory of collective excitations, for which there does not exist any published effective theory, despite being the same approximation necessary for high-temperature QED and QCD plasmas. Second, we will show that this implies that the number operator used throughout quantum field theory is actually incorrect (does not match the Fermi-Dirac distribution), and we will present a new one. The new number operator can be understood as the Pauli-blocking repulsive pseudo-force, known to exist from statistical mechanics. Finally, using a single free Weyl fermion, we will expand the interaction in auxiliary fields, and show that this imparts a Majorana mass and chemical potential to the fermion, and has s-wave collective excitations that include a complex scalar with negative mass-squared, and massless vector bosons. Time permitting we will discuss the p-wave collective excitations which include "Emergent Electroweak Gravity". We will conclude with wild speculation about what this all means and where this research is going.