Ralf Hofmann
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Ralf Hofmann has a total of 229 co-authors. Here are the top co-authors by number of shared publications:
- Julian Moosmann
Institute of Materials Physics, Helmholtz-Zentrum Hereon, Geesthacht, Germany
10 shared publications - Thierry Grandou
Institut de Physique de Nice Université Côte d'Azur UMR CNRS 7010 1361 routes des Lucioles 06560 Valbonne France
9 shared publications - Janning Meinert
Bergische Universität Wuppertal, Department of Physics, Wuppertal
7 shared publications Tilo Baumbach
Institute for Photon Science and Synchrotron Radiation, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen, Germany
6 shared publications- Carsten Hast
SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
4 shared publications H Kapitza
4 shared publications
Latest Publications
- 6 July 2026
- Published by World Scientific Pub Co Pte Ltd in Modern Physics Letters A
- Vol. 41 (34)
Spatially and scale-parameter averaged, covariant, scalar two-point correlation of the field strength on Harrington–Shepard (anti)caloron in deconfining SU(2) Yang–Mills thermodynamics
In this paper, we demonstrate that an infinite scale-parameter and spatial average over the covariant, scalar two-point correlator of the field strength on a Harrington–Shepard caloron or anticaloron is [Formula: see text] where [Formula: see text] and [Formula: see text] are indeterminate real parameters, [Formula: see text], [Formula: see text] is Euclidean time, and T denotes temperature. The selfconsistent introduction of physical infrared cutoffs for scale parameter and spatial radius in deconfining SU(2) Yang–Mills thermodynamics (and an associated fuzziness of the azimuthal angles due to small imaginary parts or small surplus/defect angles) does not alter the above, analytically obtained sine dependence in any significant way.
- 6 July 2026
- Published by World Scientific Pub Co Pte Ltd in Modern Physics Letters A
- Vol. 41 (34)
Spatially and scale-parameter averaged, covariant, scalar two-point correlation of the field strength on Harrington–Shepard (anti)caloron in deconfining SU(2) Yang–Mills thermodynamics
In this paper, we demonstrate that an infinite scale-parameter and spatial average over the covariant, scalar two-point correlator of the field strength on a Harrington–Shepard caloron or anticaloron is [Formula: see text] where [Formula: see text] and [Formula: see text] are indeterminate real parameters, [Formula: see text], [Formula: see text] is Euclidean time, and T denotes temperature. The selfconsistent introduction of physical infrared cutoffs for scale parameter and spatial radius in deconfining SU(2) Yang–Mills thermodynamics (and an associated fuzziness of the azimuthal angles due to small imaginary parts or small surplus/defect angles) does not alter the above, analytically obtained sine dependence in any significant way.
- 5 June 2026
- Published by World Scientific Pub Co Pte Ltd in International Journal of Modern Physics A
- Vol. 41 (17)
How thermal quantum pressure of free, massive and bosonic quasiparticles probes Riemann’s zeta function
A known integral representation of the quantum pressure of free, massive and bosonic quasiparticles is considered. Depending on how this integral is evaluated, the pressure can be written, modulo a power times logarithmic correction, as a convergent power series, valid for small masses, or as a rapidly convergent infinite sum over modified Bessel functions when mass is large. The derivative of this integral with respect to mass squared can be represented as an optimally truncated, exponentially asymptotic series. This series is employed to analyze the evolution of quasiparticle mass m in the deconfining phase of SU(2) Yang–Mills thermodynamics down to the critical temperature. Expanding the integral for the quantum pressure in powers of the logarithm of m yields large-n coefficients [ ] which probe Riemann’s zeta function [ ] within the critical strip [ ] at large imaginary heights. Appealing to the meromorphic nature of the integrands, we employ a saddle point approximation to estimate the large-n asymptotics of [ ] by integration along contours of steepest descent. As a result, comparisons between saddle-point estimates and localized integrations along vertical lines are facilitated to test assumed properties of [ ] within the critical strip.
- 5 June 2026
- Published by World Scientific Pub Co Pte Ltd in International Journal of Modern Physics A
- Vol. 41 (17)
How thermal quantum pressure of free, massive and bosonic quasiparticles probes Riemann’s zeta function
A known integral representation of the quantum pressure of free, massive and bosonic quasiparticles is considered. Depending on how this integral is evaluated, the pressure can be written, modulo a power times logarithmic correction, as a convergent power series, valid for small masses, or as a rapidly convergent infinite sum over modified Bessel functions when mass is large. The derivative of this integral with respect to mass squared can be represented as an optimally truncated, exponentially asymptotic series. This series is employed to analyze the evolution of quasiparticle mass m in the deconfining phase of SU(2) Yang–Mills thermodynamics down to the critical temperature. Expanding the integral for the quantum pressure in powers of the logarithm of m yields large-n coefficients [ ] which probe Riemann’s zeta function [ ] within the critical strip [ ] at large imaginary heights. Appealing to the meromorphic nature of the integrands, we employ a saddle point approximation to estimate the large-n asymptotics of [ ] by integration along contours of steepest descent. As a result, comparisons between saddle-point estimates and localized integrations along vertical lines are facilitated to test assumed properties of [ ] within the critical strip.
- Open Access
Editorial for Special Issue “Quantum Field Theory, 2nd Edition”
This second Special Issue on Quantum Field Theory is a continuation of the first Special Issue on quantum field theory
Open AccessEditorial for Special Issue “Quantum Field Theory, 2nd Edition”
This second Special Issue on Quantum Field Theory is a continuation of the first Special Issue on quantum field theory
- Open Access
Steven Weinberg’s Life for Physics
This is a personal review of Steven Weinberg’s scientific autobiography “A Life in Physics”. A reflection on both, personal aspects and scientific milestones of Professor Weinberg’s role-model life is conducted to honour his lasting accomplishments as a great physicist, academic teacher, and public activist in progressing high-energy particle theory and theoretical cosmology, and in raising public support for fundamental physics.
Open AccessSteven Weinberg’s Life for Physics
This is a personal review of Steven Weinberg’s scientific autobiography “A Life in Physics”. A reflection on both, personal aspects and scientific milestones of Professor Weinberg’s role-model life is conducted to honour his lasting accomplishments as a great physicist, academic teacher, and public activist in progressing high-energy particle theory and theoretical cosmology, and in raising public support for fundamental physics.
- Open Access
On the Yang-Mills Propagator at Strong Coupling
About twelve years ago, the use of standard functional manipulations was demonstrated to imply an unexpected property satisfied by the fermionic Green’s functions of . This non-perturbative phenomenon has been dubbed an effective locality. In a much simpler way than in , the most remarkable and intriguing aspects of effective locality have been presented in a recent publication on the Yang-Mills theory on Minkowski spacetime. While quickly recalled in the current paper, these results are used to calculate the problematic gluonic propagator in the Yang-Mills non-perturbative regime. This paper is dedicated to the memory of Professor Herbert M. Fried (1929–2023), whose inspiring manner, impressive command of functional methods in quantum field theories, enthusiasm for a broad range of topics in Theoretical Physics, and warm friendship are missed greatly by the authors.Open AccessOn the Yang-Mills Propagator at Strong Coupling
About twelve years ago, the use of standard functional manipulations was demonstrated to imply an unexpected property satisfied by the fermionic Green’s functions of . This non-perturbative phenomenon has been dubbed an effective locality. In a much simpler way than in , the most remarkable and intriguing aspects of effective locality have been presented in a recent publication on the Yang-Mills theory on Minkowski spacetime. While quickly recalled in the current paper, these results are used to calculate the problematic gluonic propagator in the Yang-Mills non-perturbative regime. This paper is dedicated to the memory of Professor Herbert M. Fried (1929–2023), whose inspiring manner, impressive command of functional methods in quantum field theories, enthusiasm for a broad range of topics in Theoretical Physics, and warm friendship are missed greatly by the authors. - Open Access
Axion Mass and the Ground State of Deconfining SU(2) Yang–Mills Thermodynamics
For the deconfinement phase of an SU(2) Yang–Mills theory, we compute the axion mass by appealing to the Veneziano–Witten formula. The topological susceptibility arises (i) from a precisely computable thermal ground-state contribution due to a center of a relevant (anti)caloron, and (ii) from contributions due to free thermal quasi-particles in the effective theory. Both (i) and (ii) are derived by using standard Euclidean thermal field theory techniques. While contribution (i) is positive and , contribution (ii) is negative, as demanded by reflection positivity, but negligible compared to contribution (i). As a consequence, practically from the critical temperature onward, a real-valued axion mass emerges when the Peccei–Quinn scale is assumed to be the Planck mass , independently of the Yang–Mills scale that the axion associates with. We discuss why our results deviate from those found in the dilute instanton gas and interacting instanton liquid approximations, and from results obtained in lattice simulations. Assuming the universe is dark sector to be based on such ultralight axion species, which are nonrelativistic for , we investigate the cosmological conditions for their global Bose condensation as the very early universe cooled to temperatures of the order of eV.Open AccessAxion Mass and the Ground State of Deconfining SU(2) Yang–Mills Thermodynamics
For the deconfinement phase of an SU(2) Yang–Mills theory, we compute the axion mass by appealing to the Veneziano–Witten formula. The topological susceptibility arises (i) from a precisely computable thermal ground-state contribution due to a center of a relevant (anti)caloron, and (ii) from contributions due to free thermal quasi-particles in the effective theory. Both (i) and (ii) are derived by using standard Euclidean thermal field theory techniques. While contribution (i) is positive and , contribution (ii) is negative, as demanded by reflection positivity, but negligible compared to contribution (i). As a consequence, practically from the critical temperature onward, a real-valued axion mass emerges when the Peccei–Quinn scale is assumed to be the Planck mass , independently of the Yang–Mills scale that the axion associates with. We discuss why our results deviate from those found in the dilute instanton gas and interacting instanton liquid approximations, and from results obtained in lattice simulations. Assuming the universe is dark sector to be based on such ultralight axion species, which are nonrelativistic for , we investigate the cosmological conditions for their global Bose condensation as the very early universe cooled to temperatures of the order of eV. - Open Access
Electroweak Parameters from Mixed SU(2) Yang–Mills Thermodynamics
Based on the thermal phase structure of pure SU(2) quantum Yang–Mills theory, we describe the electron at rest as an extended particle, a droplet of radius , where is the Bohr radius. This droplet is of vanishing pressure and traps a monopole within its bulk at a temperature of keV. The monopole is in the Bogomolny–Prasad–Sommerfield (BPS) limit. It is interpreted in an electric–magnetically dual way. Utilizing a spherical mirror-charge construction, we approximate the droplet’s charge at a value of the electromagnetic fine-structure constant of for soft external probes. It is shown that the droplet does not exhibit an electric dipole or quadrupole moment due to averages of its far-field electric potential over monopole positions. We also calculate the mixing angle , which belongs to deconfining phases of two SU(2) gauge theories of very distinct Yang–Mills scales ( keV and eV). Here, the condition that the droplet’s bulk thermodynamics is stable determines the value of . The core radius of the monopole, whose inverse equals the droplet’s mass in natural units, is about 1% of .Open AccessElectroweak Parameters from Mixed SU(2) Yang–Mills Thermodynamics
Based on the thermal phase structure of pure SU(2) quantum Yang–Mills theory, we describe the electron at rest as an extended particle, a droplet of radius , where is the Bohr radius. This droplet is of vanishing pressure and traps a monopole within its bulk at a temperature of keV. The monopole is in the Bogomolny–Prasad–Sommerfield (BPS) limit. It is interpreted in an electric–magnetically dual way. Utilizing a spherical mirror-charge construction, we approximate the droplet’s charge at a value of the electromagnetic fine-structure constant of for soft external probes. It is shown that the droplet does not exhibit an electric dipole or quadrupole moment due to averages of its far-field electric potential over monopole positions. We also calculate the mixing angle , which belongs to deconfining phases of two SU(2) gauge theories of very distinct Yang–Mills scales ( keV and eV). Here, the condition that the droplet’s bulk thermodynamics is stable determines the value of . The core radius of the monopole, whose inverse equals the droplet’s mass in natural units, is about 1% of . - Open Access
Quantum Field Theory
This Special Issue on quantum field theory presents work covering a wide and topical range of subjects mainly within the area of interacting 4D quantum field theories subject to certain backgrounds
Open AccessQuantum Field Theory
This Special Issue on quantum field theory presents work covering a wide and topical range of subjects mainly within the area of interacting 4D quantum field theories subject to certain backgrounds
- Open Access
Frequency-redshift relation of the Cosmic Microwave Background
We point out that a modified temperature-redshift relation ($T$-$z$ relation) of the cosmic microwave background (CMB) can not be deduced by any observational method that appeals to an a priori thermalisation to the CMB temperature $T$ of the excited states in a probe environment of independently determined redshift $z$. For example, this applies to quasar-light absorption by a damped Lyman-alpha system due to atomic as well as ionic fine-splitting transitions or molecular rotational bands. Similarly, the thermal Sunyaev-Zel'dovich (thSZ) effect cannot be used to extract the CMB's $T$-$z$ relation. This is because the relative line strengths between ground and excited states in the former and the CMB spectral distortion in the latter case both depend, apart from environment specific normalisations, solely on the dimensionless spectral variable $x=\frac{hν}{k_B T}$. Since literature on extractions of the CMB's $T$-$z$ relation always assumes (i) $ν(z)=(1+z)ν(z=0)$ where $ν(z=0)$ is the observed frequency in the heliocentric rest frame, the finding (ii) $T(z)=(1+z)T(z=0)$ just confirms the expected blackbody nature of the interacting CMB at $z>0$. In contrast to emission of isolated, directed radiation, whose frequency-redshift relation ($ν$-$z$ relation) is subject to (i), a non-conventional $ν$-$z$ relation $ν(z)=f(z)ν(z=0)$ of pure, isotropic blackbody radiation, subject to adiabatically slow cosmic expansion, necessarily has to follow that of the $T$-$z$ relation $T(z)=f(z)T(z=0)$ and vice versa. In general, the function $f(z)$ is determined by energy conservation of the CMB fluid in a Friedmann-Lemaitre-Robertson-Walker universe. If the pure CMB is subject to an SU(2) rather than a U(1) gauge principle, then $f(z)= \left({1/4}\right)^{1/3}(1+z)$ for $z\gg 1$, and $f(z)$ is nonlinear for $z\sim 1$.Open AccessFrequency-redshift relation of the Cosmic Microwave Background
We point out that a modified temperature-redshift relation ($T$-$z$ relation) of the cosmic microwave background (CMB) can not be deduced by any observational method that appeals to an a priori thermalisation to the CMB temperature $T$ of the excited states in a probe environment of independently determined redshift $z$. For example, this applies to quasar-light absorption by a damped Lyman-alpha system due to atomic as well as ionic fine-splitting transitions or molecular rotational bands. Similarly, the thermal Sunyaev-Zel'dovich (thSZ) effect cannot be used to extract the CMB's $T$-$z$ relation. This is because the relative line strengths between ground and excited states in the former and the CMB spectral distortion in the latter case both depend, apart from environment specific normalisations, solely on the dimensionless spectral variable $x=\frac{hν}{k_B T}$. Since literature on extractions of the CMB's $T$-$z$ relation always assumes (i) $ν(z)=(1+z)ν(z=0)$ where $ν(z=0)$ is the observed frequency in the heliocentric rest frame, the finding (ii) $T(z)=(1+z)T(z=0)$ just confirms the expected blackbody nature of the interacting CMB at $z>0$. In contrast to emission of isolated, directed radiation, whose frequency-redshift relation ($ν$-$z$ relation) is subject to (i), a non-conventional $ν$-$z$ relation $ν(z)=f(z)ν(z=0)$ of pure, isotropic blackbody radiation, subject to adiabatically slow cosmic expansion, necessarily has to follow that of the $T$-$z$ relation $T(z)=f(z)T(z=0)$ and vice versa. In general, the function $f(z)$ is determined by energy conservation of the CMB fluid in a Friedmann-Lemaitre-Robertson-Walker universe. If the pure CMB is subject to an SU(2) rather than a U(1) gauge principle, then $f(z)= \left({1/4}\right)^{1/3}(1+z)$ for $z\gg 1$, and $f(z)$ is nonlinear for $z\sim 1$. - Open Access
Frequency–Redshift Relation of the Cosmic Microwave Background
We point out that a modified temperature–redshift relation (T-z relation) of the cosmic microwave background (CMB) cannot be deduced by any observational method that appeals to an a priori thermalisation to the CMB temperature T of the excited states in a probe environment of independently determined redshift z. For example, this applies to quasar-light absorption by a damped Lyman-alpha system due to atomic as well as ionic fine-splitting transitions or molecular rotational bands. Similarly, the thermal Sunyaev-Zel’dovich (thSZ) effect cannot be used to extract the CMB’s T-z relation. This is because the relative line strengths between ground and excited states in the former and the CMB spectral distortion in the latter case both depend, apart from environment-specific normalisations, solely on the dimensionless spectral variable . Since the literature on extractions of the CMB’s T-z relation always assumes (i) , where is the observed frequency in the heliocentric rest frame, the finding (ii) just confirms the expected blackbody nature of the interacting CMB at . In contrast to the emission of isolated, directed radiation, whose frequency–redshift relation (-z relation) is subject to (i), a non-conventional -z relation of pure, isotropic blackbody radiation, subject to adiabatically slow cosmic expansion, necessarily has to follow that of the T-z relation and vice versa. In general, the function is determined by the energy conservation of the CMB fluid in a Friedmann–Lemaitre–Robertson–Walker universe. If the pure CMB is subject to an SU(2) rather than a U(1) gauge principle, then for , and is non-linear for .Open AccessFrequency–Redshift Relation of the Cosmic Microwave Background
We point out that a modified temperature–redshift relation (T-z relation) of the cosmic microwave background (CMB) cannot be deduced by any observational method that appeals to an a priori thermalisation to the CMB temperature T of the excited states in a probe environment of independently determined redshift z. For example, this applies to quasar-light absorption by a damped Lyman-alpha system due to atomic as well as ionic fine-splitting transitions or molecular rotational bands. Similarly, the thermal Sunyaev-Zel’dovich (thSZ) effect cannot be used to extract the CMB’s T-z relation. This is because the relative line strengths between ground and excited states in the former and the CMB spectral distortion in the latter case both depend, apart from environment-specific normalisations, solely on the dimensionless spectral variable . Since the literature on extractions of the CMB’s T-z relation always assumes (i) , where is the observed frequency in the heliocentric rest frame, the finding (ii) just confirms the expected blackbody nature of the interacting CMB at . In contrast to the emission of isolated, directed radiation, whose frequency–redshift relation (-z relation) is subject to (i), a non-conventional -z relation of pure, isotropic blackbody radiation, subject to adiabatically slow cosmic expansion, necessarily has to follow that of the T-z relation and vice versa. In general, the function is determined by the energy conservation of the CMB fluid in a Friedmann–Lemaitre–Robertson–Walker universe. If the pure CMB is subject to an SU(2) rather than a U(1) gauge principle, then for , and is non-linear for .