SU(2) Yang-Mills thermodynamics: a priori estimate and radiative corrections

We review and explain essential characteristics of the a priori estimate of the thermal ground state and its excitations in the deconfining phase of SU(2) Quantum Yang-Mills thermodynamics. This includes the spatially central and peripheral structure of Harrington-Shepard (anti)calorons, a sketch on how a spatial coarse-graining over (anti)caloron centers yields an inert scalar field, which is responsible for an adjoint Higgs mechanism, the identification of (anti)caloron action with $\hbar$, a discussion of how, owing to (anti)caloron structure, the thermal ground state can be excited (wave-like and particle-like massless modes, massive thermal quasiparticle fluctuations), the principle role of and accounting for radiative corrections, the exclusion of energy-sign combinations due to constraints on momenta transfers in four-vertices in a completely fixed, physical gauge, dihedral diagrams and their resummation up to infinite loop order in the massive sector, and the resummation of the one-loop polarisation tensor of the massless modes. We also outline applications of deconfining SU(2) Yang-Mills thermodynamics to the Cosmic Microwave Background (CMB) which affect the cosmological model at high redshifts, the redshift for re-ionization of the Universe, the CMB angular power spectra at low $l$, and the late-time emergence of intergalactic magnetic fields.