Quantum Fields, Cosmological Constant and Symmetry Doubling

We explore how energy-parity, a protective symmetry for the cosmological constant Kaplan and Sundrum, 2005], arises naturally in the classical phase space dynamics of matter.We derive and generalize the Liouville operator of electrodynamics, incorporating a “varying alpha” and diffusion.In this model, a one-parameter deformation connects classical ensemble and quantum field theory. PACS:03.65.Ta, 03.70+k, 05.20.-y