arXiv subjects

Ralf Hofmann

Publications and source records attributed to Ralf Hofmann.

At least 37 records · Page 2Linked to original sources

arXiv2017

On the non-perturbative realization of QCD gauge-invariance

A few years ago the use of standard functional manipulations was demonstrated to imply an unexpected property satisfied by the fermionic Green's functions of QCD: effective locality. This feature of QCD is non-perturbative as it results from a full integration of the gluonic degrees of freedom. In this paper, previous derivations of effective locality are reviewed, corrected, and enhanced. Focussing on the way non-abelian gauge invariance is realized in the non-perturbative regime of QCD, the deeper meaning of effective locality is discussed.

hep-th↗

arXiv2017

SU(2)$_{\tiny\mbox{CMB}}$ at high redshifts and the value of $H_0$

We investigate a high-$z$ cosmological model to compute the co-moving sound horizon $r_s$ at baryon-velocity freeze-out towards the end of hydrogen recombination. This model assumes a replacement of the conventional CMB photon gas by deconfining SU(2) Yang-Mills thermodynamics, three flavours of massless neutrinos ($N_ν=3$), and a {\sl purely baryonic} matter sector (no cold dark-matter (CDM)). The according SU(2) temperature-redshift relation of the CMB is contrasted with recent measurements appealing to the thermal Sunyaev-Zel'dovich effect and CMB-photon absorption by molecular rotations bands or atomic hyperfine levels. Relying on a realistic simulation of the ionization history throughout recombination, we obtain $z_*=1693.55\pm 6.98$ and $z_{\rm drag}=1812.66\pm 7.01$. Due to considerable widths of the visibility functions in the solutions to the associated Boltzmann hierarchy and Euler equation we conclude that $z_*$ and $z_{\rm drag}$ over-estimate the redshifts for the respective photon and baryon-velocity freeze-out. Realistic decoupling values turn out to be $z_{{\rm lf},*}=1554.89\pm 5.18$ and $z_{\rm lf,drag}=1659.30\pm 5.48$. With $r_s(z_{\rm lf,drag})=(137.19\pm 0.45)\,$Mpc and the essentially model independent extraction of $r_s\cdot H_0=\mbox{const}$ from low-$z$ data in arXiv:1607.05617 we obtain a good match with the value $H_0=(73.24\pm 1.74)\,$km\,s$^{-1}$\,Mpc$^{-1}$ extracted in arXiv:1604.01424 by appealing to Cepheid calibrated SNe~Ia, new parallax measurements, stronger constraints on the Hubble flow, and a refined computation of distance to NGC4258 from maser data. We briefly comment on a possible interpolation of our high-$z$ model, invoking percolated and unpercolated U(1) topological solitons of a Planck-scale axion field, to the phenomenologically successful low-$z$ $Λ$CDM cosmology.

physics.gen-ph↗

arXiv2017

Massive loops in thermal SU(2) Yang-Mills theory: Radiative corrections to the pressure beyond two loops

We device an efficient book-keeping of excluded energy-sign and scattering-channel combinations for the loop four-momenta associated with massive quasi-particles, circulating in (connected) bubble diagrams subject to vertex constraints inherited from the thermal ground state. The according radiative corrections modify the free thermal-quasiparticle pressure at one loop. Increasing the loop order in two-particle irreducible (2PI) bubble diagrams, we exemplarily demonstrate a suppressing effect of the vertex constraints on the number of valid combinations. This increasingly strong suppression gave rise to the conjecture in hep-th/0609033 that the loop expansion would terminate at a finite order. Albeit the low-temperature dependence of the 2PI 3-loop diagram complies with this behaviour, a thorough analysis of the high-temperature situation reveals that the leading power in temperature is thirteen such that this diagram dominates all lower loop orders for sufficiently high temperatures. An all-loop-order resummation of 2PI diagrams with dihedral symmetry is thus required, defining an extremely well-bounded analytical continuation of the low-temperatures result.

hep-th↗

arXiv2016

SU(2) Yang-Mills Theory: Waves, Particles, and Quantum Thermodynamics

We elucidate how Quantum Thermodynamics at temperature $T$ emerges from pure and classical SU(2) Yang-Mills theory on a four-dimensional Euclidean spacetime slice $S_1\times {\bf R}^3$. 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) particle-like excitations thereof.

physics.gen-ph↗

arXiv2015

Thermal ground state and nonthermal probes

The Euclidean formulation of SU(2) Yang-Mills thermodynamics admits periodic, (anti)selfdual solutions to the fundamental, classical equation of motion which possess one unit of topological charge: (anti)calorons. A spatial coarse graining over the central region in a pair of such localised field configurations with trivial holonomy generates an inert adjoint scalar field $ϕ$, effectively describing the pure quantum part of the thermal ground state in the induced quantum field theory. Here we show for the limit of zero holonomy how (anti)calorons associate a temperature independent electric permittivity and magnetic permeability to the thermal ground state of SU(2)$_{\tiny\mbox{CMB}}$, the Yang-Mills theory conjectured to underlie photon propagation.

hep-th↗

arXiv2015

Electromagnetic waves and photons

We explore how the thermal ground states of two mixing and pure SU(2) Yang-Mills theories, SU(2)$_{\tiny\mbox{CMB}}$ of scale $Λ_{\tiny\mbox{CMB}}\sim 10^{-4}\,$eV and SU(2)$_{e}$ of scale $Λ_{e}\sim 5\times 10^5\,$eV, associate either wave or particle aspects to electromagnetic disturbances during thermalisation towards the photon gas of a blackbody, in realising the photoelectric effect, and through the frequency dependence of the monochromatic, nonthermal beam structure in Thomson/Compton scattering.

physics.gen-ph↗

arXiv2015

Relic photon temperature versus redshift and the cosmic neutrino background

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 $T_0\sim 2.725\,$K (SU(2)$_{\tiny{CMB}}$), 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 ($z_{\tiny{re}}\sim 11$) and quasar spectra ($z_{\tiny{re}}\sim 6$) is repealed. Also, we find that the redshift of CMB decoupling moves from $z_{\tiny{dec}}\sim 1100$ to $z_{\tiny{dec}}\sim 1775$ which questions $Λ$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$_{\tiny{eff}}\sim 3.36$ extracted from Planck data. Interactions between cosmic neutrinos and the CMB implies a {\sl common} temperature $T$ of (no longer separately conserved) CMB and neutrino fluids. N$_{\tiny{eff}}\sim 3.36$ then entails a universal, temperature induced cosmic neutrino mass $m_ν=ξT$ with $ξ=3.973$. Our above results on $z_{\tiny{re}}$ and $z_{\tiny{dec}}$, derived from SU(2)$_{\tiny{CMB}}$ alone, are essentially unaffected when including such a neutrino sector.

physics.gen-ph↗

arXiv2014

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

For a deconfining thermal SU(2) Yang-Mills plasma we discuss the role of (anti)calorons in introducing non-thermal behavior effectively described in terms of Planck's quantum of action $\hbar$. This non-thermality cancels exactly between the ground-state estimate and its free quasiparticle excitations. Kinematic constraints in 4-vertex scattering and the counting of radial loop variables versus the number of independent constraints on them are re-visited. Next, we consider thermal 2$\rightarrow$ 2 one-loop scattering of the modes remaining massless upon the (anti)caloron induced adjoint Higgs mechanism (thermal ground state after spatial coarse graining). Starting with stringent analytical arguments, we are able to exclude the contribution to photon-photon scattering from diagrams containing at least one three-vertex and, in a next step, a vast majority of all possible configurations involving two four-vertices. By numerical analysis we show that the remaining contribution of the overall S channel is severely suppressed compared to that of the T and U channels, meaning that the creation of a pair of massive vector modes by a pair of photons and vice versa practically does not occur in the Yang-Mills plasma. For the T and U channels the domain of loop integration represents less than $10^{-7}$ times the volume of the unconstrained integration region. The thus introduced photon-photon correlation should affect the Cosmic Microwave Background's polarisation at low redshift. An adaption of the here-developed methods to the analysis of irreducible bubble diagrams could prove the conjecture of hep-th/0609033 on the termination of the loop expansion of thermodynamical quantities at a finite irreducible order.

physics.gen-ph↗

arXiv2013

Thermodynamics of SU(2) quantum Yang-Mills theory and CMB anomalies

A brief review of effective SU(2) Yang-Mills thermodynamics in the deconfining phase is given, including the construction of the thermal ground-state estimate in terms of an inert, adjoint scalar field $ϕ$, based on non-propagating (anti)selfdual field configurations of topological charge unity. We explain why the screening physics of an SU(2) photon is subject to an electric-magnetically dual interpretation. Next, we elucidate how a low-frequency excess of line temperature in the Cosmic Microwave Background (CMB) determines the value of the critical temperature of the deconfining-preconfining phase transition of an SU(2) Yang-Mills theory postulated to describe photon propagation, and we describe how, starting at a redshift of about unity, SU(2) photons collectively work 3D temperature depressions into the CMB. Upon projection along a line of sight, a given depression influences the present CMB sky in a cosmologically local way, possibly explaining the large-angle anomalies confirmed recently by the Planck collaboration. Finally, six relativistic polarisations residing in the SU(2) vector modes roughly match the number of degrees of freedom in cosmic neutrinos (Planck) which would disqualify the latter as radiation. Indeed, if interpreted as single center-vortex loops in confining phases of SU(2) Yang-Mills theories neutrino mass $m_ν$ solely arises by interactions with an environment. Cosmologically, the CMB represents this environment, and thus one would expect that $m_ν=ξT$ where $ξ=O(1)$. In this model cosmic neutrinos are a small dark-matter contribution, conserved only together with the CMB fluid, influencing Baryonic Acoustic Oscillations during CMB decoupling.

physics.gen-ph↗

arXiv2012

Fundamental and effective SU(2) Yang-Mills vertices

Calorons and plane waves within and in between them {\sl collectively} give rise to a thermal ground state. The latter provides a homgeneous energy density and a negative pressure, and it induces quasiparticle masses to part of the propagating spectrum of deconfining SU(2) Yang-Mills thermodynamics (dynamical gauge-symmetry breaking). In the present talk we discuss the role of a {\sl single} caloron in inducing effective local vertices, characterized by powers of $\hbar$, mediating the interaction of plane waves which propagate over large distances. The constraints on momentum transfers through effective 4-vertices are revisited.

physics.gen-ph↗

arXiv2012

Charge-density waves in deconfining SU(2) Yang-Mills thermodynamics

At one-loop accuracy we compute, characterize, and discuss the dispersion laws for the three low-momentum branches of propagating longitudinal, electric U(1) fields in the effective theory for the deconfining phase of pure SU(2) Yang-Mills thermodynamics. With an electric-magnetically dual interpretation of SU(2)$_{\tiny CMB}$ we argue that upon a breaking of plasma isotropy and homogeneity, introduced e.g. by a temperature gradient, the longitudinal modes could conspire to provide magnetic seed fields for magneto-hydrodynamical dynamos inside structures of galaxy, galaxy-cluster, and cosmological scales. Such a scenario ultimately links structure with seed-field formation. As judged from the present cosmological epoch, the maximally available coherent field strength of 10$^{-8}$\,Gauss from SU(2)$_{\tiny CMB}$ matches with the upper bound for cosmological present-day field strength derived from small-angle anisotropies of the cosmic microwave background.

hep-th↗

arXiv2012

The quantum of action and finiteness of radiative corrections: Deconfining SU(2) Yang-Mills thermodynamics

The quantum of action $\hbar$, 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 {\sl fundamental} plane waves when the momentum transfer is increased away from the scale of maximal, {\sl 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.

physics.gen-ph↗

arXiv2011

Thermal Ground State in Yang-Mills Thermodynamics

We derive an a useful priori estimate for the thermal ground state of deconfining phase of SU(2) Yang-Mills thermodynamics in four-dimensional, flat spacetime and discuss its implications. Upon a selfconsistent spatial coarse-graining over noninteracting, trivial-holonomy (BPS saturated) (anti)calorons of unit topological charge modulus an inert, adjoint scalar field $|ϕ|$ and an effective pure-gauge configuration $a_μ^{gs}$ emerge. The modulus $|ϕ|>0$ defines the maximal resolution in the coarse-grained theory and induces dynamical gauge-symmetry breaking. Thanks to perturbative renormalizability and the fact that |phi| can not absorb or emit energy-momentum the effective action is local and simple. The temperature dependence of the effective coupling is a consequence of thermodynamical consistency and describes the Coulomb screening of a static test charge due to short-lived monopole-antimonopole pairs. The latter occur unresolvably as small-holonomy excitations of (anti)calorons by the absorption of propagating fundamental gauge fields.

hep-th↗

arXiv2010

Improved ground-state estimate by thermal resummation

For the deconfining phase of SU(2) Yang-Mills thermodynamics and for high temperatures we point out that a linear dependence on temperature of a one-loop selfconsistently resummed thermal correction to the pressure and the energy density takes place despite a quartic dependence arising from an unsummed two-loop correction. This linearity is hierarchically smaller than the one belonging to the tree-level estimate of the thermal ground-state. We discuss and interprete this result.

hep-th↗

arXiv2010

Modification of black-body radiance at low temperatures and frequencies

In contrast to earlier reports, where the spectrum of the {\sl energy density} of photonic black-body radiation modified by SU(2) effects was discussed, we discuss the low-frequency spectrum of the {\sl radiance} at temperatures ranging between 5 and 20 Kelvin. We conclude that compared to the conventional theory the only observable effect is associated with the spectral gap (total screening). We also discuss how a low-temperature black body cavity under the influence of a sufficiently strong static electric field is forced to emit according to Planck's radiation law (pure U(1) theory) even at low frequencies and how this effect can be utilized to measure SU(2) induced deviations.

hep-ph↗

arXiv2009

Spatial Wilson loop in continuum, deconfining SU(2) Yang-Mills thermodynamics

The uniquess of the effective actions describing 4D SU(2) and SU(3) continuum, infinite-volume Yang-Mills thermodynamics in their deconfining and preconfining phases is made explicit. Subsequently, the spatial string tension is computed in the approach proposed by Korthals-Altes. This SU(2) calculation is based on a particular, effective two-loop correction to the pressure needed for the extraction of the hypothetic number density of isolated and screened magnetic monopoles or antimonopoles in the deconfining phase. By exponentiating the exchange of the tree-level massless but one-loop dressed mode within a quadratic spatial contour of side-length $L$ in the effective theory we demonstrate that for $L\to\infty$ the Wilson loop exhibits {\sl perimeter} law. This is in contrast to a rigorous {\sl lattice} result subject to the Wilson action and for this action valid at sufficiently high temperature. In the framework of the effective theory there is, however, a regime for small (spatially unresolved) $L$ were the exponent of the spatial Wilson loop possesses curvature as a function of $L$.

hep-th↗

arXiv2009

Yang-Mills thermodynamics

We present a quantitative analysis of Yang-Mills thermodynamics in 4D flat spacetime. The focus is on the gauge group SU(2). Results for SU(3) are mentioned in passing. Although all essential arguments and results were reported elsewhere we summarize them here in a concise way and offer a number of refinements and some additions.

hep-th↗

arXiv2009

Loop expansion in Yang-Mills thermodynamics

We argue that a selfconsistent spatial coarse-graining, which involves interacting (anti)calorons of unit topological charge modulus, implies that real-time loop expansions of thermodynamical quantities in the deconfining phase of SU(2) and SU(3) Yang-Mills thermodynamics are, modulo 1PI resummations, determined by a finite number of connected bubble diagrams.

hep-th↗