arXiv subjects

Manfried Faber

Publications and source records attributed to Manfried Faber.

At least 19 recordsLinked to original sources

arXiv2026

High-precision lattice determination of the interaction potential of an SU(2) solitonic dipole and comparison with perturbative QED

We determine the interaction potential of a solitonic dipole in the singlet state, modeled as an SU(2) field, using improved lattice simulations of two stationary solitons at varying separations. The potential is extracted from the energy of two-soliton configurations as a function of distance. At large separations, the interaction reproduces the classical Coulomb potential quantitatively up to an energy shift $\delta E_\infty\approx 9\;\text{keV}$ of the fitted asymptotic constant relative to $2m_ec_0^2$, assumed to be related to limited numerical precision on the lattice. At shorter distances, deviations from the Coloumb potential of point-like charges appear, that are in qualitative agreement with the asymptotic formula of perturbative Quantum Electrodynamics, reflecting the running of the fine-structure constant, with the inverse fine-structure constant ($\alpha^{-1} \approx 137$) reproduced.

hep-lat↗

arXiv2025

Against the point-like nature of the electron

Experts in quantum field theory (QFT) generally answer the question of the ``size of an electron'' with ``point-like''. On the other hand, QFT recognizes quantum effects, shielding by virtual particles, the so-called polarization cloud, which should describe the size of physical electrons. Scattering experiments with electrons, such as those carried out in high-energy experiments at particle accelerators, should be able to clarify whether physical electrons are really point-like, as claimed by experts and in textbooks. In this article, I show that both the formulas of QFT and the corresponding cross sections are consistent with an extent of the electron of the size of the classical electron radius. The assumption that the relativistic energy of electrons in the high-energy limit consists solely of deformation energy from the extended electron density distribution allows for a simple interpretation of the experimental cross sections. For this reason, I refer to classical models in 1+1 and 3+1 dimensions that have precisely this property. The difference between the terms point-like, structureless, and substructureless is highlighted. The usual objections to the claim that the electron radius is finite and has already been measured in electron scattering experiments are discussed.

physics.gen-ph↗

arXiv2025

Conclusions Not Yet Drawn from the Unsolved 4/3-Problem -- How to Get a Stable Classical Electron

It has been known for over 100 years that there is a discrepancy between Maxwell's electrodynamics and the idea of a classical electron as the ``atom'' of electricity. This incompatibility is known under the terms 4/3 problem of the classical electron and radiation reaction force and was circumvented in the currently most successful theories, the quantum field theories, by limit value considerations, by the mutual subtraction of infinities, i.e., by purely mathematical methods that eliminate obvious contradictions but are not really based on an intuitive understanding of its physical causes. The actual origin of the problems mentioned lies in the instability of the classical electron. Stabilization cannot be achieved within the framework of Maxwell's electrodynamics. This raises the question of what a minimal change to the fundamentals of electrodynamics should look like, which contains Maxwell's theory as a limiting case. A detailed analysis of the 4/3 problem points to models that fulfill these requirements.

physics.gen-ph↗

arXiv2024

What do we know about the confinement mechanism?

Color confinement is a fundamental phenomenon in quantum chromodynamics. In this work, the mechanisms underlying color confinement are investigated in detail, with a particular focus on the role of non-perturbative phenomena such as center vortices and monopoles in the QCD vacuum. By exploring lattice QCD approaches, including the Maximal Center Gauge and center projection methods, we examine how these topological structures contribute to the confining force between color charges. We also address the limitations of conventional methods and suggest improvements to the gauge fixing prescription to enhance the accuracy of string tension predictions. Our findings support the validity of the center vortex model as a key candidate for understanding the dynamics of the confining QCD vacuum.

hep-lat↗

arXiv2024

Investigation of the ensemble of maximal center gauge

Maximal Center Gauge (MCG) aims to detect center vortices by maximizing a gauge functional and then projecting onto the center elements of the respective group. The requirement for unrestricted maximization of the gauge functional has proven to be untenable because it was shown that it leads to an underestimation of the string tension. To counter this problem, the ensemble of local gauge maxima is investigated and it is found that the unrestricted maximization can be replaced by a maximization restricted to the Gaussian distributed part of the ensemble. Such restricted maximization weakens the problem of an underestimated string tension.

hep-lat↗

arXiv2023

Calorons, monopoles and stable, charged solitons

We discuss the similarity of the constituent monopoles of calorons and stable topological solitons with long range Coulombic interaction, classical solutions of the model of topological particles. In the interpretation as electric charges they can be compared to electrons and positrons with spin up and down, with quantised charge and finite mass.

hep-lat↗

arXiv2023

Stationary Schr\"odinger Equation and Darwin Term from Maximal Entropy Random Walk

We describe particles in a potential by a special diffusion process, the maximal entropy random walk (MERW) on a lattice. Since MERW originates in a variational problem, it shares the linear algebra of Hilbert spaces with quantum mechanics. The Born rule appears from measurements between equilibrium states in the past and the same equilibrium states in the future. Introducing potentials by the observation that time, in a gravitational field running in different heights with a different speed, MERW respects the rule that all trajectories of the same duration are counted with equal probability. In this way, MERW allows us to derive the Schr\"odinger equation for a particle in a potential and the Darwin term of the nonrelativistic expansion of the Dirac equation. Finally, we discuss why quantum mechanics cannot be simply a result of MERW, but, due to the many analogies, MERW may pave the way for further understanding.

quant-ph↗

arXiv2023

A first analysis of the ensemble of local maxima of maximal center gauge

Maximal center gauge (MCG) aims to detect some of the most important vacuum configurations, suggesting thick magnetic flux tubes quantised to non-trivial center elements of the gauge group being responsible for confinement. Due to the NP-hardness of a global maximization of the gauge functional only numeric procedures aiming for local maxima are possible. We observe a linear decrease of the string tension with increasing gauge functional value of the local maxima. This implies that the request to get as close as possible to the absolute maximum is untainable. We compare global properties of the ensemble of local maxima with other methods to detect center vortices and with determinations of the string tension from full configurations. This comparison indicates that the information about the number and positions of center vortices is contained in the structure of the ensemble of local maxima. This may pave the way for a future more successful formulation of the gauge condition.

hep-lat↗

arXiv2022

Numerical Evaluation of a Soliton Pair with Long Range Interaction

Within the model of topological particles (MTP) we determine the interaction energy of monopole pairs, sources and sinks of a Coulombic field. The monopoles are represented by topological solitons of finite size and mass, described by a field without any divergences. We fix the soliton centres in numerical calculations at varying distance. Due to the finite size of the solitons we get deviations from the Coulomb potential at distances of a few soliton radii. We compare the numerical results for these deviations with the running of the coupling in perturbative QED.

hep-lat↗

arXiv2022

From soft Dirac monopoles to the Dirac equation

In the model of topological particles we have four types of topologically stable dual Dirac monopoles with soft core and finite mass. We discuss the steps how to get a Dirac equation for these particles. We show for the free and the interacting case that we arrive at the Dirac equation in the limit, where the soft solitons approach singular dual Dirac monopoles.

physics.gen-ph↗

arXiv2022

A geometric model in 3+1D space-time for electrodynamic phenomena

With the idea to find geometric formulations of particle physics we investigate the predictions of a three dimensional generalisation of the Sine-Gordon model, very close to the Skyrme model and to the Wu-Yang description of Dirac monopoles. With three rotational degrees of freedom of spatial Dreibeins we formulate a Lagrangian and confront the predictions to electromagnetic phenomena. Stable solitonic excitations we compare with the lightest fundamental electric charges, electrons and positrons. Two Goldstone bosons we relate to the properties of photons. These particles are characterised by three topological quantum numbers, which we compare to charge, spin and photon number. Finally we conjecture some ideas for further comparisons with experiments.

physics.gen-ph↗

arXiv2021

Spectra of Neutron Wave Functions in Earth's Gravitational Field

The time evolution of a quantum wave packet in the linear gravity potential is known as Quantum Bouncing Ball. The qBounce collaboration recently observed such a system by dropping wave packets of ultracold neutrons by a height of roughly 30 microns. In this article, space and momentum spectra as well as Wigner functions of the neutron wave functions in the gravitational field of the Earth are analyzed. We investigate the quantum states in the "preparation region", into which they transition after exiting a narrow double-mirror system and where we would expect to observe free fall and bounces in classical physics. For this, we start from the stationary solutions and eigenvalues of the Schr\"odinger equation in terms of Airy functions and their zeros. Subsequently, we examine space and momentum distributions as well as Wigner functions in phase space for pure and mixed quantum states. The eventual influence of Yukawa-like forces for small distances of several micrometers from the mirror is included through first order perturbation calculations. Those allow us to study the resulting modifications of space and momentum distributions, and phase space functions.

quant-ph↗

arXiv2021

About the solution of the numerical instability for topological solitons with long range interaction

The computations of solutions of the field equations in the Model of Topological Particles, formulated with a scalar SU(2)-field, have shown instabilities leading to discrepancies between the numerical and analytical solutions. We identify the origin of these deviations in misalignments of the rotational axes corresponding to the SU(2) elements. The system of a single soliton we use as an example to show that a constraint suppressing the wave-like disturbances is able to lead to excellent agreement between the result of the numerical minimisation procedure and the analytical solution.

hep-lat↗

arXiv2021

The road to solving the Gribov problem of the center vortex model in quantum chromo dynamics

The center vortex model of the QCD vacuum is very successful in explaining the non-perturbative properties of QCD, especially confinement, chiral symmetry breaking and the topological charge of vacuum configurations. On the other hand, the center vortex model still suffers from a Gribov problem: Direct maximal center gauge and center projection can lead to an underestimation of the string tension in smooth configurations or after persistent simulated annealing. We discuss methods to identify center regions, whose boundaries evaluate to center elements, and want to improve the vortex detection: these regions might help to recognize vortices in configurations where maximal center gauge lost the vortex finding property.

hep-lat↗

arXiv2021

Center regions as a solution to the Gribov problem of the center vortex model

The center vortex model, capable of explaining confinement and chiral symmetry breaking, has been plagued by the lattice equivalent of Gribov copies: different maxima of the gauge functional lead to different predictions of the string tension. It is possible to resolve this problem using center regions, loops evaluating to center elements, as guide for the gauge fixing procedure. The success of this approach was already shown, but the algorithms came with an arbitrary free parameter. In recent development this parameter has been fixed, even improving the results.

hep-lat↗

arXiv2019

Improving center vortex detection by usage of center regions as guidance for the direct maximal center gauge

The center vortex model of quantum chromodynamic states that vortices, closed color-magnetic flux, percolate the vacuum. Vortices are seen as the relevant excitations of the vacuum, causing confinement and dynamical chiral symmetry breaking. In an appropriate gauge, as \textit{direct maximal center gauge}, vortices are detected by projecting onto the center degrees of freedom. Such gauges suffer from Gribov copy problems: different local maxima of the corresponding gauge functional can result in different predictions of the string tension. By using non-trivial center regions, that is, regions whose boundary evaluates to a non-trivial center element, a resolution of this issue seems possible. We use such non-trivial center regions to guide simulated annealing procedures, preventing an underestimation of the string tension in order to resolve the Gribov copy problem.

hep-lat↗

arXiv2019

Influence of Fermions on Vortices in SU(2)-QCD

Gauge fields control the dynamics of fermions, also a back reaction of fermions on the gauge field is expected. This back reaction is investigated within the vortex picture of the QCD vacuum. We show that the center vortex model reproduces the string tension of the full theory also with the presence of fermionic fields.

hep-lat↗

arXiv2019

Chiral Symmetry Breaking on the Lattice

We review important aspects of QCD in the continuum and on the lattice and take a look at the fate of its symmetries with an emphasis on chiral symmetry breaking on the lattice.

hep-lat↗