The Quantum of Action and Finiteness of Radiative Corrections: Deconfining SU(2) Yang-Mills Thermodynamics

The quantum of action , multiplying in certain powers perturbative vertices in 4D gauge theory, is related to the action of just-not-resolved selfdual and thermal gauge field configurations, calorons and anticalorons, of charge modulus unity. Appealing to the derivation of the effective theory for the deconfining phase of SU(2) Yang-Mills thermodynamics, we conclude that these vertex inducers convey a rapidly decreasing interaction strength between { fundamental} plane waves when the momentum transfer is increased away from the scale of maximal, { effective} resolution. This adds a deeper justification to the renormalization programme of perturbation theory which ignores the contribution to the partition function of nontrivially selfdual configurations. We also point out a connection between the QED fine-structure constant α and the electric-magnetically dual of the effective gauge coupling in the deconfining phase, and we illustrate the workings of effective loops in the expansion of the pressure.