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

Abstract

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.

The isolated, uniformly moving electron: Selfintersecting SU(2) Yang-Mills center vortex loop and Louis de Broglie’s hidden thermodynamics

“…On the other hand, the Yang-Mills coupling e was argued to be e = √ 8π √ almost everywhere in the deconfining phase [14], based on the observation in [15] that only a small range of (anti)caloron radii, centered about the spatial coarse-graining cutoff |φ| −1 , contributes to the emergent thermal ground state. This value of e implies the (anti)caloron action to be .…”

Thermal Ground State and Nonthermal Probes

“…Its modulus |φ| sets the maximal possible resolution in the effective theory whose ground state energy density essentially is given as tr Λ 6 φ 2 = 4πΛ 3 T (Λ a constant of integration of dimension mass) and whose propagating sector is, in a totally fixed, physical gauge (unitary-Coulomb) characterised by a massless mode (γ, unbroken U(1) subgroup of SU(2)) and two thermal quasiparticle modes of equal mass m = 2e |φ| (V ± , mass induced by adjoint Higgs mechanism) which propagate thermally, that is, on-shell only. Interactions within this propagating sector are mediated by isolated (anti)calorons whose action is argued to be [7,8]. Judged in terms of inclusive quantities such as radiative corrections to the oneloop pressure or the energy density of blackbody radiation, these interactions are feeble [9], and their expansion into 1-PI irreducible bubble diagrams is conjectured to terminate at a finite number of loops [12].…”

One-loop photon–photon scattering in a thermal, deconfining SU(2) Yang–Mills plasma

“…Effective, indeterministic behavior, inherent to scattering amplitudes in quantum Yang-Mills theory, appears to be associated with the presence of classical field configurations of finite action and nontrivial topology in 4D Euclidean spacetime [1,2,3,4]. For SU (2) Yang-Mills thermodynamics a concrete argument in favor of this idea was put forward recently [5,6]. Namely, in its deconfining phase an adjoint Higgs mechanism, caused by calorons and anicalorons of topological charge modulus unity, which, upon spatial coarse graining [7], effectively materialize in terms of an inert scalar field φ, splits the Yang-Mills mass spectrum into two degenerate modes propagating on their quasiparticle mass-shell (unitary gauge) and a massless mode (photon) whose off-shellness is constrained by |φ| (Coulomb gauge) [8].…”

“…For the deconfining phase of SU(2) Yang-Mills thermodynamics we have in [5,6] identified the Euclidean action of relevant calorons or anticalorons [14,15,16,17] with . The according chain of arguments relies on a Minkowskian interpretation of free but effectively massive (adjoint Higgs mechanism) one-loop fluctuations about the ground-state estimate.…”

“…Thermodynamic consistency (linking of thermodynamical quantities by Legendre transformations motivated by the left part of Eq. (1)) and a dimensional counting in effective interaction monomials with appropriately normalized field variables [19] determines the effective coupling e in units of −1/2 [5,6]. Finally, one appeals to the observation that (anti)caloron radii ρ ∼ |φ| −1 dominate the spatial coarse-graining -generating the field φ [7,18] -to justify the use of e in the formula S = 8π 2 e 2 for the Euclidean action of the fundamental field configurations caloron or anticaloron with topological charge modulus unity 1 .…”