The Thermodynamics of Quantum Yang-Mills Theory

Hofmann, Ralf

doi:10.1142/9789814329972

Cited by 29 publications

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“…At the critical temperature G vanishes and equation (1) reduces to the usual energy-momentum relation of a massless photon. For T T c , the thermal mass is small, but negative.…”

Section: Modified Black Body Spectramentioning

confidence: 99%

“…Based on these results, we state a postulate, from which these results have direct relevance to a gas of photons. A detailed derivation and discussion can be found in [1], and an overview in last year's ICNAAM presentations [2].In Yang-Mills thermodynamics, calorons of trivial [3] and nontrivial [4,5] holonomy are non-perturbative, finite action solutions to the equations of motion. By performing a spatial average over non-interacting calorons [6], the non-perturbative ground-state can be described by a macroscopic adjoint scalar field φ with modulus |φ | = Λ 3 /2πT .…”

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“…To determine the value of T c , we note that the cosmic microwave background radiation, as the prime example of a thermalized photon gas, exhibits an almost perfect black body spectrum. This then gives T c ≡ T CMB 2.73 K. A more detailed discussion on the value of T c can be found in [1]. Another important aspect is that the role of the electric and magnetic fields in the mathematical SU(2)are interchanged when applied to SU(2) CMB photon physics [7].…”

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Applications of Yang-Mills thermodynamics

Schwarz¹

2012

AIP Conference Proceedings

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We discuss the postulate that the U(1) gauge group describing photon propagation results from a dynamically broken SU(2) gauge theory. In the context of Yang-Mills thermodynamics such a symmetry breaking occurs via the nontrivial ground state. As a result of the interaction with the quasi particles of the theory the photon acquires an effective, temperature and momentum dependent, mass. We explain how this leads to modified black body spectra at temperatures of about 5 K. Furthermore, we discuss the properties and effects of an emergent longitudinal polarization.In this section we briefly repeat some key results of the non-perturbative approach to SU(2)Yang-Mills thermodynamics. Based on these results, we state a postulate, from which these results have direct relevance to a gas of photons. A detailed derivation and discussion can be found in [1], and an overview in last year's ICNAAM presentations [2].In Yang-Mills thermodynamics, calorons of trivial [3] and nontrivial [4,5] holonomy are non-perturbative, finite action solutions to the equations of motion. By performing a spatial average over non-interacting calorons [6], the non-perturbative ground-state can be described by a macroscopic adjoint scalar field φ with modulus |φ | = Λ 3 /2πT . Here, T and Λ denote the temperature and Yang-Mills scale, respectively. The field φ does not fluctuate and acts as a background for the topological trivial sector of the theory [7].The investigation of propagating gauge modes is done by a transformation to unitary gauge [7]. It is then seen that the SU(2)-symmetry is dynamically broken down to U(1) by φ . The theory then contains one tree-level massless (TLM) mode interacting with two tree-level heavy (TLH) modes. The mass of the latter is given by m = 2e |φ | and depends on temperature. The effective gauge coupling e(T ) is a function of temperature, and exhibits a logarithmic pole at the critical temperature T c = 13.87Λ/2π as well as a plateau value of √ 8π for T Λ. In spite of this large value for the coupling constant a loop expansion of thermodynamical quantities shows rapid conversion due to compositeness constraints [8]. POSTULATE ABOUT PHOTONS AND SU(2) CMBAlthough massless on tree-level, the calculation of the one-loop polarization tensor of the TLM mode [9] reveals that it acquires a temperature dependent mass, due to the interaction with the TLH modes. But since the mass of the TLH modes diverges at T c , they decouple from the TLM mode at this temperature. This implies that the TLM mode is exactly massless at T c only. It is this property that allows for a connection to photon physics via the following postulate [7]. Namely, the photon is postulated to be the TLM mode of a new gauge group, called SU(2) CMB . To determine the value of T c , we note that the cosmic microwave background radiation, as the prime example of a thermalized photon gas, exhibits an almost perfect black body spectrum. This then gives T c ≡ T CMB 2.73 K. A more detailed discussion on the value of T c can be found in [1]. Another important ...

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“…At the critical temperature G vanishes and equation (1) reduces to the usual energy-momentum relation of a massless photon. For T T c , the thermal mass is small, but negative.…”

Section: Modified Black Body Spectramentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Applications of Yang-Mills thermodynamics

Schwarz¹

2012

AIP Conference Proceedings

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“…Driven by the short-range nature of the weak interactions, gauge-symmetry breaking was introduced into the SMPP in the framework of the Glashow-Salam-Weinberg theory in terms of an SU(2) fundamentally charged scalar (Higgs) field subject to a renormalisable selfinteraction. Such a Higgs sector, however, only vaguely represents the phase structure and associated gauge-symmetry breaking patterns of the pure and nonperturbatively approached Yang-Mills theory [16]. The nonperturbative a priori estimate of each phase's ground state in the latter case clearly links to its (gapped or ungapped) excitations, thereby ruling both classical and quantum radiative behaviour in distinct spectral domains [16].…”

Section: Introductionmentioning

confidence: 99%

SU(2) Quantum Yang-Mills Thermodynamics: Some Theory and Some Applications

Hofmann¹

2018

Preprint

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In the first part of this talk we review some prerequisites for and essential arguments involved in the construction of the thermal-ground-state estimate underlying the deconfining phase in the thermodynamics of SU(2) Quantum Yang-Mills theory and how this structure supports its distinct excitations. The second part applies deconfining SU(2) Yang-Mills thermodynamics to the Cosmic Microwave Background in view of (i) a modified temperature-redshift relation with an interesting link to correlation-length criticality in the 3D Ising model, (ii) the implied minimal changes in the dark sector of the cosmological model, and (iii) best-fit parameter values of this model when confronted with the spectra of the angular two-point functions TT, TE, and EE, excluding the low-l physics. The latter, which so far is treated in an incomplete way due to the omission of radiative effects, is addressed in passing.

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Relic photon temperature versus redshift and the cosmic neutrino background

Hofmann

2015

Annalen der Physik

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Presuming that CMB photons are described by the deconfining phase of an SU(2) Yang-Mills theory with the critical temperature for the deconfining-preconfining phase transition matching the present CMB temperature T 0 ∼ 2.725 K (SU(2) CMB ), we investigate how CMB temperature T connects with the cosmological scale factor a in a Friedmann-Lemaître-Robertson-Walker Universe. Owing to a violation of conformal scaling at late times, the tension between the (instantaneous) redshift of reionisation from CMB observation (z re ∼ 11) and quasar spectra (z re ∼ 6) is repealed. Also, we find that the redshift of CMB decoupling moves from z dec ∼ 1100 to z dec ∼ 1775 which questions CDM cosmology at high redshifts. Adapting this model to the conventional physics of three flavours of massless cosmic neutrinos, we demonstrate inconsistency with the value N eff ∼ 3.36 extracted from Planck data. Interactions between cosmic neutrinos and the CMB implies a common temperature T of (no longer separately conserved) CMB and neutrino fluids. N eff ∼ 3.36 then entails a universal, temperature induced cosmic neutrino mass m ν = ξ T with ξ = 3.973. Our above results on z re and z dec , derived from SU(2) CMB alone, are essentially unaffected when including such a neutrino sector.

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The Thermodynamics of Quantum Yang-Mills Theory

Cited by 29 publications

References 0 publications

Applications of Yang-Mills thermodynamics

Applications of Yang-Mills thermodynamics

SU(2) Quantum Yang-Mills Thermodynamics: Some Theory and Some Applications

Relic photon temperature versus redshift and the cosmic neutrino background

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