Thermal Ground State and Nonthermal Probes

From the source

1. In the Euclidean formulation of SU(2) Yang-Mills thermodynamics, a spatial coarse graining over the central region of a pair of localised, periodic, self-dual and antiself-dual solutions carrying one unit of topological charge — calorons and anticalorons of trivial holonomy — generates an inert adjoint scalar field. That field effectively describes the pure quantum part of the thermal ground state in the induced quantum field theory, and the ground state's energy density is four pi times the cube of the Yang-Mills scale times the temperature.Abstract; Section 2, Sketch of Deconfining SU(2) Yang-Mills Thermodynamics

2. The structure of a Harrington-Shepard caloron depends on how far from its centre you look, and the paper works out both regimes. At distances larger than the inverse temperature but smaller than a characteristic separation, the fields are those of a static non-Abelian monopole carrying unit electric and magnetic charge — a dyon. Further out than that separation, the same configuration is a static, self-dual non-Abelian dipole whose dipole moment is set by that separation itself.Section 3.3, Anatomy of a Relevant Harrington-Shepard Caloron, equations 8 to 11

3. For a probe wave whose wavelength is much longer than the dipole separation, dividing the dipole density carried by the ground state by the probe's own field strength gives the electric permittivity and magnetic permeability of the vacuum — and the result carries no temperature dependence and therefore no dependence on the probe's field strength. Grandou and Hofmann state the consequence directly: ’It is a universal constant. In particular, it does not relate to the state of fictitious ground-state thermalisation which would associate with the rest frame of a local heat bath.’Section 4.1, Preexisting Dipole Densities, equations 15 to 21

4. Setting the calculated permittivity equal to the measured value fixes the charge of the non-Abelian monopole constituting the dipole at 19.56 times the elementary electron charge. In the authors' words: ’Thus, compared to the electron charge, the charge unit associated with a (anti)self-dual non-Abelian dipole, residing in the thermal ground state, is gigantic.’Section 4.1, equation 22

5. The theory being applied is SU(2)CMB — the postulate that thermal photon propagation follows an SU(2) rather than a U(1) gauge principle, with a Yang-Mills scale of about 1.0638 times ten to the minus fourth electron volts fixed by low-frequency observation of the cosmic microwave background so that the deconfining to preconfining critical temperature equals the microwave background's present baseline temperature of 2.725 kelvin.Section 4, Thermal Ground State as Induced by a Probe, opening paragraph

6. The picture has a stated edge, and the authors name it. The ground state supports a nonthermal probe purely in terms of trivial-holonomy calorons only when an uncertainty-like relation between the wavelength and the fourth power of the probe's field strength is obeyed; the two regimes give minimum wavelengths of 1.1254 metres and 0.112 metres, a factor of ten apart. Shorter wavelengths or higher intensities would require additional, mixing SU(2) gauge factors of hierarchically larger Yang-Mills scales, and the authors say it is not yet clear how the Standard Model's success would be recovered from such a framework.Sections 4.3 and 5, equations 23, 33 and 34

The way in

How to cite it

Thierry Grandou, Ralf Hofmann (2015) Thermal Ground State and Nonthermal Probes doi:10.1155/2015/197197

Where it sits in the curriculum

• What the vacuum is