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Benjamin Koch

Publications and source records attributed to Benjamin Koch.

At least 37 records · Page 2Linked to original sources
arXiv2022

Corrections to the Gyromagnetic Factor in Very Special Relativity

We consider Very Special Relativity corrections to the energy spectrum of a $C-$invariant Dirac Fermion in a static and homogeneous magnetic field $\vec B$. First, in the case of $\vec B$ parallel to the spatial VSR preferred direction $\vec n$, finding that the expression for the energy spectrum stays the same, except for a correction to the mass arising from the VSR contribution. Then, we relax the parallelism condition, finding a new equation for the energy spectrum. We solve this equation perturbatively. With a Penning trap's experiment in mind, we derive the first order VSR corrections to the electron's $g-2$ factor. Finally, using the current errors on the electron's $g$-factor measurements in Penning trap's experiments, we obtain an upper bound to the VSR electron mass parameter, and therefore also to the VSR electronic neutrino mass, of $0.824 \, eV$. This result does not contradict the possibility for VSR to be the origin of neutrino masses.

hep-ph↗
arXiv2022

The stepwise path integral of the relativistic point particle

In this paper we present a stepwise construction of the path integral over relativistic orbits in Euclidean spacetime. It is shown that the apparent problems of this path integral, like the breakdown of the naive Chapman-Kolmogorov relation, can be solved by a careful analysis of the overcounting associated with local and global symmetries. Based on this, the direct calculation of the quantum propagator of the relativistic point particle in the path integral formulation results from a simple and purely geometric construction. paperpitch https://www.youtube.com/watch?v=tNMbCgPbq2A

hep-th↗
arXiv2022

Polarization-Dependent Loss of Optical Connectors Measured with High Accuracy (<0.004 dB) after Cancelation of Polarimetric Errors

State-of-the-art polarimeter calibration is reviewed. Producing many quasi-random polarization states and moving/bending a fiber without changing power allows finding a polarimeter calibration where the degree-of-polarization reaches unity and parasitic polarization-dependent loss is small. Using a polarization scrambler/transformer and a polarimeter a device-under-test can be characterized. Its Mueller matrix can be decomposed into a product of a nondepolarizing Mueller-Jones matrix times a purely depolarizing Mueller matrix. Test polarizations may drift over time. With help of an optical switch the reference device can be measured against an internal reference path. Later, with possibly different test polarizations, the actual device-under-test is measured against the internal reference. Polarization drift and need for repeated reference device measurement are thus overcome. When a patchcord is inserted, connector PDL can be measured, provided that errors are calibrated away, again by fiber moving/bending. Experimentally we have measured PDL with errors <0.004 dB. This easily suffices to measure connector PDL, which is demonstrated. PDL >60 dB was measured when the device under test was a good polarizer. A 20 Mrad/s polarization scrambler with LiNbO3 device generates the test polarizations. The polarimeter can sample at 100 MHz and can store 64M Stokes vectors. During laser frequency scans Mueller matrices can be measured in time intervals as short as 5 us.

physics.optics↗
arXiv2022

Statefinder analysis of scale-dependent cosmology

We study the statefinder parameters of a cosmological model based on scale-dependent gravity. The effective Einstein field equations come from an average effective action. From the dynamical system, we derive analytical expressions that improve the convergence of the numerical solutions. We determine the statefinder parameters for moderate redshift and compare them with well-known alternatives to $Λ$CDM.

gr-qc↗
arXiv2022

Almost relevant corrections for direct measurements of electron's g-factor

We revisit the observable used for the direct measurements of the electron's $g$ factor. This is done by considering the sub-leading effects of the large magnetic background field and virtual Standard Model processes. We find substantial corrections to the Landau levels of the electron. Implications for the observed magnetic moment and the tension between direct and indirect measurement are discussed.

hep-ph↗
arXiv2021

Can scale-dependent cosmology alleviate the $H_0$ tension?

Scale-dependence is a common feature to all effective models of quantum gravity. In this paper, a cosmological model based on the scale-dependent scenario of gravity is presented. It is argued that such models, where the scale-dependence appears as a correction to the classical $Λ$CDM evolution, have the potential of addressing the tensions between early and late time measurements of $H_0$. After defining criteria to parametrize this tension, we perform a numerical scan over the parameter space of the scale-dependent model, subject to these criteria. In this analysis, it is found that, indeed, the tension can be released.

gr-qc↗
arXiv2021

Path integral of the relativistic point particle in Minkowski space

In this article, we analyze the fundamental global and local symmetries involved in the action for the free relativistic point particle. Moreover, we identify a hidden local symmetry, whose explicit consideration and factorization utilizing of a Fujikawa prescription, leads to the construction of relativistic propagators that satisfy the Chapman-Kolmogorov identity. By means of a detailed topological analysis, we find three different relativistic propagators (orthochronous, space-like, and Feynman) which are obtained from the exclusive integration of paths within different sectors in Minkowski space. Finally, the connection of this approach to the Feynman checkerboard construction is explored.

hep-th↗
arXiv2021

Four dimensional Einstein-power-Maxwell black hole solutions in scale-dependent gravity

In the present work, we extend and generalize our previous work regarding the scale dependence applied to black holes in the presence of non-linear electrodynamics [1]. The starting point for this study is the Einstein-power-Maxwell theory with a vanishing cosmological constant in (3+1) dimensions, assuming a scale dependence of both the gravitational and the electromagnetic coupling. We further examine the corresponding thermodynamic properties and how these quantities experience deviations from their classical counterparts. We solve the effective Einstein's field equations using the "null energy condition" to obtain analytical solutions. The implications of quantum corrections are also briefly discussed. Finally, we analyze our solutions and compare them to related results in the literature.

gr-qc↗
arXiv2021

A technique for natural gauge boson masses

In this work, a novel mechanism for spontaneous symmetry breaking is presented. This mechanism avoids quadratic divergencies and is thus capable of addressing the hierarchy problem in gauge theories. Using the scale-dependent effective action $Γ_{k}$ minimally coupled to a gravitational sector, variational parameter setting is applied. This provides a mass and vacuum expectation value as a function of the constants arising in the low scale expansion of Newtons' and cosmological couplings. A comparison with experimental data, such as the Higgs mass, allows putting restrictions on these constants. With this generic approach one can compare with explicit candidates for an effective field theory of gravity. As an example, we use the asymptotic safety scenario, where we find restrictions on the matter content of the theory.

hep-th↗
arXiv2020

X17: A new force, or evidence for a hard $γ+γ$ process?

It is investigated whether the "X17 puzzle" might be explained by a nuclear decay chain and a conversion of the two resulting highly energetic $γ$s into an electron-positron pair. It is found that the corresponding kinematics fits perfectly to the experimental result. Also the conversion rates of this process are reasonable. However, the assumed nuclear chain reaction is not favored in the established nuclear models and no explanation for the isospin structure of the signal can be given. Thus, it has to be concluded that the process studied in this paper does not give a completely satisfying explanation of the "X17 puzzle".

hep-ph↗
arXiv2020

Black hole shadow of a rotating scale--dependent black hole

In this work, starting from a spherically symmetric scale--dependent black hole, a rotating solution is obtained by following the Newman--Janis algorithm without complexification. Besides studying the horizon, the static conditions and causality issues of the rotating solution, we get and discuss the shape of its shadow.

gr-qc↗
arXiv2020

Electromagnetic stress on nucleon structure

External electromagnetic fields can provoke stress, and thus modifications of the internal structure of nucleons. Working with this hypothesis, one can derive a simple description of the charge dependence of the EMC effect. This first result is confirmed by two explicit models of the structure functions of deformed nucleons in the atomic nucleus. For large nuclei a continuous model is used. For small nuclei a discrete distribution of nuclear matter gives better results.

nucl-th↗
arXiv2020

Scale-dependent rotating BTZ black hole

This work presents a generalization of the rotating black hole in two plus one dimensions, in the light of scale--dependent gravitational couplings. In particular, the gravitational coupling $κ_0$ and the cosmological term $Λ_0$ are not forced to be constants anymore. Instead, $κ$ and $Λ$ are allowed to change along the radial scale $r$. The effective Einstein field equations of this problem are solved by assuming static rotational symmetry and by maintaining the usual structure of the line element. For this generalized solution, the asymptotic behavior, the horizon structure, and the thermodynamic properties are analyzed.

hep-th↗
arXiv2019

Cosmological constant problem: deflation during inflation

We argue that the discrepancy between the Planck mass scale and the observed value of the cosmological constant can be largely attenuated if those quantities are understood as a result of effective, and thus scale-dependent, couplings. We exemplify this mechanism for the early inflationary epoch of the universe by solving the corresponding effective gap equations, subject to an energy condition. Several non-trivial checks and extensions are discussed. A comparison of our results to the renormalization group flow, obtained within the asymptotic safety program reveals a stunning agreement.

gr-qc↗
arXiv2019

Geometric Description of Schrödinger Equation in Finsler and Funk Geometry

For a system of $n$ non-relativistic spinless bosons, we show by using a set of suitable matching conditions that the quantum equations in the pilot-wave limit can be translated into a geometric language for a Finslerian manifold. We further link these equations to Euclidean timelike relative Funk geometry and show that the two different metrics in both of these geometric frameworks lead to the same coupling.

gr-qc↗
arXiv2019

Structure and Needed Properties of Reasonable Polarization Mode Dispersion Emulators for Coherent Optical Fiber Transmission

This paper proposes a scientifically reasonable polarization mode dispersion (PMD) emulator (PMDE) for coherent optical fiber transmission. Guidelines are physically correct modeling of the polarization-dispersive fiber, the time-variable polarization transformations occurring in there, including emulation of polarization events caused by lightning strikes, the adoption of acceptable compromise to keep implementation cost low enough and competitive industrial basis for production of such PMDE. We propse a PMDE consisting of N differential group delay (DGD) sections placed between N+1 time-variable general retarders or polarization scramblers. These should be general elliptical retarders, capable of changing polarization with rates up to 20 Mrad/s on the Poincaré sphere. That should include bursts of polarization rotations forth and back at up to 20 Mrad/s. The DGD sections can be fixed or variable and should be able to constitute a total PMD of alternatively, say, 20 ps, 50 ps, 100 ps, 200 ps, or another set of various discrete values. We propose even N and equal individual DGDs, which allows the total PMDE to assume a neutral state without any PMD of whatever order. Number N may be chosen relatively small; N = 2 seems acceptable. A variety of component and subsystem suppliers is available, and the proposed PMDE is available on the market.

eess.SP↗