The quantum of action and finiteness of radiative corrections: Deconfining SU(2) Yang-Mills thermodynamics

TL;DR

This paper links the quantum of action to selfdual gauge configurations in SU(2) Yang-Mills thermodynamics, providing insights into the decreasing interaction strength at high momenta and supporting the renormalization approach that neglects certain configurations.

Contribution

It offers a novel interpretation of the quantum of action through calorons and anticalorons, and connects the effective gauge coupling to the fine-structure constant in the deconfining phase.

Findings

Interaction strength decreases with increasing momentum transfer.

Justifies ignoring nontrivially selfdual configurations in perturbative expansions.

Connects the effective gauge coupling to the QED fine-structure constant.

Abstract

The quantum of action $\hbar$, 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 {\sl fundamental} plane waves when the momentum transfer is increased away from the scale of maximal, {\sl 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 $\alpha$ 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.