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Ralf Hofmann

Publications and source records attributed to Ralf Hofmann.

At least 73 records · Page 4Linked to original sources
arXiv2007

Nonperturbative screening of the Landau pole

Based on the trace anomaly for the energy-momentum tensor, an effective theory for the thermodynamics of the deconfining phase, and by assuming the asymptotic behavior to be determined by one-loop perturbation theory we compute the nonperturbative beta function for the fundamental coupling $g$ in SU(2) and SU(3) Yang-Mills theory. With increasing temperature we observe a very rapid approach to the perturbative running. The Landau pole is nonperturbatively screened.

hep-th↗
arXiv2006

Nonperturbative approach to Yang-Mills thermodynamics

An analytical and nonperturbative approach to SU(2) and SU(3) Yang-Mills thermodynamics is developed and applied. Each theory comes in three phases: A deconfining, a preconfining, and a confining one. We show how macroscopic and inert scalar fields form in each phase and how they determine the ground-state physics and the properties of the excitations. While the excitations in the deconfining and preconfining phase are massless or massive gauge modes the excitations in the confining phase are massless or massive spin-1/2 fermions. The nature of the two phase transitions is investigated for each theory. We compute the temperature evolution of thermodynamical quantities in the deconfining and preconfining phase and estimate the density of states in the confining phase. Some implications for particle physics and cosmology are discussed.

hep-th↗
arXiv2006

A strongly interacting SU(2) pure gauge theory and the nature of light

We present quantitative and qualitative arguments in favor of the claim that, within the present cosmological epoch, the U(1)$_Y$ factor in the Standard Model is an effective manifestation of SU(2) pure gauge dynamics of Yang-Mills scale $Λ\sim 10^{-4}$ eV. Results for the pressure and the energy density in the deconfining phase of this theory, obtained in a nonperturbative and analytical way, support this connection in view of large-angle features inherent in the map of the CMB temperature fluctuations and temperature-polarization cross correlations.

hep-ph↗
arXiv2006

Yang-Mills thermodynamics: The deconfining phase

We summarize recent nonperturbative results obtained for the thermodynamics of an SU(2) and an SU(3) Yang-Mills theory being in its deconfining (electric) phase. Emphasis is put on an explanation of the concepts involved. The presentation of technical details is avoided.

hep-th↗
arXiv2006

Yang-Mills thermodynamics: The preconfining phase

We summarize recent nonperturbative results obtained for the thermodynamics of an SU(2) and an SU(3) Yang-Mills theory being in its preconfining (magnetic) phase. We focus on an explanation of the involved concepts and derivations, and we avoid technical details.

hep-th↗
arXiv2006

Yang-Mills thermodynamics: The confining phase

We summarize recent nonperturbative results obtained for the thermodynamics of an SU(2) and an SU(3) Yang-Mills theory being in its confining (center) phase. This phase is associated with a dynamical breaking of the local magnetic center symmetry. Emphasis is put on an explanation of the involved concepts.

hep-th↗
arXiv2006

Gap in the black-body spectrum at low temperature

We postulate that the U(1)$_Y$ factor of the Standard Model is an effective manifestation of SU(2) gauge dynamics being dynamically broken by nonperturbative effects. The modified propagation properties of the photon at low temperatures and momenta are computed. As a result of strong screening, the presence of a sizable gap in the spectral power of a black body at temperatures $T=5... 20 $K and for low frequencies is predicted: A table-top experiment should be able to discover this gap. If the gap is observed then the Standard Model's mechanism for electroweak symmetry-breaking is endangered by a contradiction with Big-Bang nucleosynthesis. Based on our results, we propose an explanation for the stability of cold, old, dilute, and large clouds of atomic hydrogen in between spiral arms of the outer galaxy.

hep-ph↗
arXiv2006

A Planck-scale axion and SU(2) Yang-Mills dynamics: Present acceleration and the fate of the photon

From the time of CMB decoupling onwards we investigate cosmological evolution subject to a strongly interacting SU(2) gauge theory of Yang-Mills scale $Λ\sim 10^{-4}$ eV (masquerading as the $U(1)_{Y}$ factor of the SM at present). The viability of this postulate is discussed in view of cosmological and (astro)particle physics bounds. The gauge theory is coupled to a spatially homogeneous and ultra-light (Planck-scale) axion field. As first pointed out by Frieman et al., such an axion is a viable candidate for quintessence, i.e. dynamical dark energy, being associated with today's cosmological acceleration. A prediction of an upper limit $Δt_{m_γ=0}$ for the duration of the epoch stretching from the present to the point where the photon starts to be Meissner massive is obtained: $Δt_{m_γ=0}\sim 2.2$ billion years.

hep-th↗
arXiv2006

The deconfining phase of SU(2) Yang-Mills thermodynamics

We present an overview on nonperturbative thermodynamics in the deconfining phase of an SU(2) Yang-Mills theory. In a unique effective theory the maximal resolution of trivial-topology fluctuations is constrained by coarse-grained, interacting calorons and anticalorons. Loop expansions of thermodynamical quantities are discussed. Postulating that SU(2)$_{\tiny{CMB}}\stackrel{\tiny{today}}=U(1)_Y$, a modification of thermalized, low-momentum photon propagation is predicted for temperatures a few times that of the cosmic microwave background. We discuss phenomenological implications: magnetic-field induced dichroism and birefringence at a temperature of 4.2 K (PVLAS), stability of cold and dilute clouds of atomic hydrogen in our galaxy, and absence of low-$l$ correlations in the TT CMB power spectrum.

hep-th↗
arXiv2006

Radiative corrections to the pressure and the one-loop polarization tensor of massless modes in SU(2) Yang-Mills thermodynamics

We compute the one-loop polarization tensor $Π$ for the on-shell, massless mode in a thermalized SU(2) Yang-Mills theory being in its deconfining phase. Postulating that SU(2)$_{\tiny{CMB}}\stackrel{\tiny{today}}=U(1)_Y$, we discuss $Π$'s effect on the low-momentum part of the black-body spectrum at temperatures $\sim 2... 4$ $T_{\tiny{CMB}}$ where $T_{\tiny{CMB}}\sim 2.73 $K. A table-top experiment is proposed to test the above postulate. As an application, we point out a possible connection with the stability of dilute, cold, and old innergalactic atomic hydrogen clouds. We also compute the two-loop correction to the pressure arising from the instantaneous massless mode in unitary-Coulomb gauge, which formerly was neglected, and present improved estimates for subdominant corrections.

hep-th↗
arXiv2006

Explosive Z Pinch

We propose an explanation for the recently observed powerful contained explosion in a Z pinch experiment performed at Sandia National Laboratories. Our arguments are based on the assumption that a pure SU(2) Yang-Mills theory of scale $\sim 0.5 $MeV is responsible for the emergence of the electron and its neutrino.

hep-ph↗
arXiv2005

Asymptotic Freedom and Compositeness

We compute the phase and the modulus of an energy- and pressure-free, composite, adjoint, and inert field $ϕ$ in an SU(2) Yang-Mills theory at large temperatures. This field is physically relevant in describing part of the ground-state structure and the quasiparticle masses of excitations. The field $ϕ$ possesses nontrivial $S^1$-winding on the group manifold $S^3$. Even at asymptotically high temperatures, where the theory reaches its Stefan-Boltzmann limit, the field $ϕ$, though strongly power-suppressed, is conceptually relevant: its presence resolves the infrared problem of thermal perturbation theory.

hep-th↗
arXiv2004

Analytical approach to SU(2) Yang-Mills thermodynamics

We propose an analytical approach to SU(2) Yang-Mills thermodynamics. The existence of a macroscopic and rigid adjoint Higgs field, generated by dilute trivial-holonomy calorons at large temperature $T$ (electric phase), implies a twofold degeneracy of the ground state which signals a broken electric $Z_2$ symmetry. A finite energy density $\propto T$ of the ground state arises due to caloron interaction. An evolution equation for the effective gauge coupling, derived from thermodynamical self-consistency, predicts a second-order like transition (seen in lattice simulations) at $T_c$ to a phase where monopoles are condensed and off-Cartan excitations decoupled. In this magnetic phase the ground state is unique and dominates the pressure (negative total pressure). While the magnetic phase has a massive, propagating 'photon' it confines fundamental matter (pre-confinement). The temperature dependence of the magnetic gauge coupling predicts the transition to the confining phase at $T_C\sim \frac{T_c}{1.9}$ where center-vortex loops condense and the 'photon' decouples. We believe that this transition is 'swallowed' by finite-size artefacts in lattice simulations. No thermodynamical connection exists between the confining and the magnetic phase.

hep-ph↗
arXiv2004

Spontaneously broken, local Z$_2$ symmetry and the anatomy of a lepton

In the framework of the gauge symmetry ${SU(2)}_{\tiny{CMB}}\times {SU(2)}_{\tiny{e}}\times {SU(2)}_{\tinyμ}\times {SU(2)}_{\tinyτ}$ we provide a microscopic argument why a spontaneously broken, local Z$_2$ symmetry surviving the 1$^{\tiny{st}}$ order phase transition to the confining phase of one of the SU(2) factors generates two stable spin-1/2 excitations of vastly different mass. A mixture of Fermi-Dirac and Bose-Einstein distributions with the former favored by a factor two over the latter is obtained by applying inequivalent, local-in-Euclidean-time Z$_2$ transformations to one and the same field configuration contained in the description of the center-vortex condensate.

hep-ph↗
arXiv2004

A thermal theory for charged leptons

We propose that charged leptons are the `baryons' of the gauge dynamics subject to a SU(2)$_{e}$$\timesSU(2)_μ\timesSU(2)_τ$ symmetry. The `mesons' of this theory are neutral and thus candidates for dark matter. There is, in addition, a gauge group SU(2)$_{\tiny{CMB}}$ generating the CMB photon. We {\sl compute} the value of $α_{\tiny{em}}$ and the contribution to $\La_{\tiny{cosmo}}$ coming from SU(2)$_{\tiny{CMB}}$. We qualitatively explain the occurrence of dark matter, large intergalactic magnetic fields, a lepton asymmtry, the stability of $T_{\tiny{CMB}}$, and the deviation from thermal QED behavior of hot plasmas present in the interior of the sun and terrestial nuclear fusion experiments.

hep-ph↗
arXiv2004

Pointlike electrons and muons and the nature of neutrinos

We show that the form factor of an electron or a muon is unity for the modulus of the momentum transfer away from the Hagedorn temperatures $T^{e}_0\sim m_e$ and $T^μ_0\sim m_μ$ and lower than the hadronic Hagedorn temperature $T^{\tiny{QCD}}_0\sim m_π$. The structure of the electron or the muon is resolved for momemtum transfers comparable to $T^{e,μ}_0$. This is seen in scattering experiments performed in the 1950s, 1960s, and early 1970s to test the validity of QED. We interprete center-vortex loops with no self-intersection, occurring in the confining phases of each SU(2) gauge-theory factor, as {\sl Majorana} neutrinos. We offer a possible explanation for a contribution to $Λ_{\tiny{cosmo}}$ not generated by the so-far nonconfining, strongly interacting gauge theory SU(2)$_{\tiny{CMB}}$.

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