SU(2) Yang–Mills Theory: Waves, Particles, and Quantum Thermodynamics
Hofmann, Ralf
Abstract (englisch):
We elucidate how Quantum Thermodynamics at temperature T emerges from pure and classical SU(2)
SU(2) Yang–Mills theory on a fourdimensional Euclidean spacetime slice S1×R3.The concept of a (deconfining) thermal ground state, composed of certain solutions to the fundamental, classical Yang–Mills equation, allows for a unified addressation of both (classical) wave and (quantum) particlelike excitations thereof. More definitely, the thermal ground state represents the interplay between nonpropagating, periodic configurations which are electricmagnetically (anti)selfdual in a nontrivial way and possess topological charge modulus unity. Their trivialholonomy versions—Harrington–Shepard (HS) (anti)calorons—yield an accurate a priori estimate of the thermal ground state in terms of spatially coarsegrained centers, each containing one quantum of action ℏ localized at its inmost spacetime point, which induce an inert adjoint scalar field ϕ ( ϕ spatiotemporally constant). The field ϕ , in turn, implies an effective puregauge configuration, a gs μ , accurately describing HS (anti)caloron overlap. Spatial homogeneity of the thermal groundstate estimate ϕ,a gs μ demands that (anti)caloron centers are densely packed, thus representing a collective departure from (anti)selfduality. Effectively, such a “nervous” microscopic situation gives rise to two static phenomena: finite groundstate energy density ρ gs and pressure P gs with ρ gs =−P gs as well as the (adjoint) Higgs mechanism. The peripheries of HS (anti)calorons are static and resemble (anti)selfdual dipole fields whose apparent dipole moments are determined by ϕ and T, protecting them against deformation potentially caused by overlap. Such a protection extends to the spatial density of HS (anti)caloron centers. Thus the vacuum electric permittivity ϵ 0 and magnetic permeability μ 0, supporting the propagation of wavelike disturbances in the U(1) Cartan subalgebra of SU(2), can be reliably calculated for disturbances which do not probe HS (anti)caloron centers. Both ϵ 0 and μ 0 turn out to be temperature independent in thermal equilibrium but also for an isolated, monochromatic U(1) wave. HS (anti)caloron centers, on the other hand, react onto wavelike disturbances, which would resolve their spatiotemporal structure, by indeterministic emissions of quanta of energy and momentum. Thermodynamically seen, such events are Boltzmann weighted and occur independently at distinct locations in space and instants in (Minkowskian) time, entailing the Bose–Einstein distribution. Small correlative ramifications associate with effective radiative corrections, e.g., in terms of polarization tensors. We comment on an SU(2) × SU(2) based gaugetheory model, describing wave and particlelike aspects of electromagnetic disturbances within the so far experimentally/observationally investigated spectrum.
Zugehörige Institution(en) am KIT 
Institut für Photonenforschung und Synchrotronstrahlung (IPS)

Publikationstyp 
Zeitschriftenaufsatz 
Jahr 
2016 
Sprache 
Englisch 
Identifikator 
DOI: 10.3390/e18090310
ISSN: 10994300
URN: urn:nbn:de:swb:90594290
KITopen ID: 1000059429 
Erschienen in 
Entropy 
Band 
18 
Heft 
9 
Seiten 
310 
Bemerkung zur Veröffentlichung 
Gefördert durch den KITPublikationsfonds

Schlagworte 
Harrington–Shepard caloron; (anti)selfduality; electric and magnetic dipole densities; vacuum permittivity and permeability; Poincaré group; quantum of action; Boltzmann weight; Bose–Einstein distribution function 