arXiv subjects

Herbert Weigel

Publications and source records attributed to Herbert Weigel.

At least 19 recordsLinked to original sources

arXiv2026

Vacuum Polarization Energy of a Nonzero Radius Cosmic String

We calculate the vacuum polarization energy (VPE) of a scalar field in the background of a nonsingular cosmic string in $2+1$ spacetime dimensions. Our calculation expresses the VPE as a renormalized sum and integral over scattering data, which can be expressed in terms of Legendre and Bessel functions for the "ballpoint pen" model, analogous to a square well in curvature, and which can be obtained numerically for a generic string profile. We show how relationships between the local density of states, expressed in terms of the Green's function, and the global density of states, expressed in terms of the Jost function, extend to this curved spacetime background and allow for precise implementation of perturbative renormalization conditions.

hep-th↗

arXiv2025

Examples for BPS solitons destabilized by quantum effects

We investigate serval models for two scalar fields in one space dimension with topologically stable solitons that are constructed from BPS equations. The asymptotic behavior of these solitons fully determines their classical energies. A particular feature of the considered mode ls is that there are several translationally invariant ground states that we call primary and secondary vacua. The former are those that ar e asymptotically assumed by the solitons. Solitons that occupy a secondary vacuum in finite but eventually large portions of space are clas sically degenerate. hus the quantum contributions to the energies are decisive for the energetically favored soliton. While some of these s olitons were constructed previously, we, for the first time, compute the leading (one-loop) quantum contribution their energies. In all ca ses considered we find that this contribution is not bounded from below and that it is the more negative the larger the region is in which the soliton approaches a secondary vacuum. This corroborates the conjecture, earlier inferred from the Shifman-Voloshin soliton, that the a vailability of secondary vacua destabilizes these solitons on the quantum level.

hep-th↗

arXiv2025

Chiral Solitons

Generalizing quantum chromodynamics (QCD) from three to arbitrarily many color degrees of freedom suggests that baryons can be described as solitons in an effective meson theory whose interaction strength decreases with the number of colors. The exact form of that theory is unknown, but at low energies chiral symmetry and its breaking are considered as the construction recipes for modeling the theory. The Skyrmion is a static, localized solution in a non-linear field theory for pions and it is the most prominent version of a soliton in a chirally symmetric meson theory. Upon quantization it reproduces the spectrum of the low-lying baryons and their static properties reasonably well. Extending that theory by vector mesons improves on the agreement between predicted and empirical data. Chiral solitons within models for the quark flavor dynamics facilitate the investigation of nucleon structure functions. Here we provide a pedagogical overview of these facets.

hep-ph↗

arXiv2024

Vacuum Polarization Energy of a Proca Soliton

We study an extended Proca model with one scalar field and one massive vector field in one space and one time dimensions. We construct the soliton solution and subsequently compute the vacuum polarization energy (VPE) which is the leading quantum correction to the classical energy of the soliton. For this calculation we adopt the spectral methods approach which heavily relies on the analytic properties of the Jost function. This function is extracted from the interaction of the quantum fluctuations with a background potential generated by the soliton. Particularly we explore eventual non-analytical components that may be induced by mass gaps and the unconventional normalization for the longitudinal component of the vector field fluctuations. By numerical simulation we verify that these obstacles do actually not arise and that the real and imaginary momentum formulations of the VPE yield equal results. The Born approximation to the Jost function is crucial when implementing standard renormalization conditions. In this context we solve problems arising from the Born approximation being imaginary for real momenta associated with energies in the mass gap.

hep-th↗

arXiv2024

One-Loop Quantum Stress-Energy Tensor for the Kink and sine-Gordon Solitons

We compute the renormalized one-loop quantum corrections to the energy density $T_{00}(x)$ and pressure $T_{11}(x)$ for solitons in the $1+1$ dimensional scalar sine-Gordon and kink models. We show how precise implementation of counterterms in dimensional regularization resolves previously identified discrepancies between the integral of $T_{00}(x)$ and the known correction to the total energy.

hep-th↗

arXiv2023

Variational Approach to Excited Fermions on Kinks

We study the back-reaction of fermion fields on the kink solution in one space and one time dimension. We employ a variational procedure to determine an upper limit for the minimum of the total energy. This energy has three contributions: the classical kink energy, the energy of valence fermions and the fermion vacuum polarization energy. The latter arises from the interaction of the kink with the Dirac sea and is required for consistency of the semi-classical expansion for the fermions. Earlier studies only considered the valence part and observed a substantial back-reaction. This was reflected by a sizable distortion of the kink profile. We find that this distortion is strongly mitigated when the Dirac sea is properly accounted for. As a result the back-reaction merely produces a slight squeeze or stretch of the kink profile.

hep-th↗

arXiv2023

Phonons scattering off discrete asymmetric solitons in the absence of a Peierls-Nabarro potential

We analyze the interaction of lattice vibrations (phonon wave-packets) with an asymmetric kink soliton initially at rest. We employ the $\phi^6$ model in one space and one time dimensions for various lattice spacings and consider two different discretization prescriptions for the field potential that do not generate Peierls-Nabarro potentials, i.e. the kink can be placed anywhere along the lattice beyond discrete translational invariance. Since the $\phi^6$ model kink is neither symmetric nor anti-symmetric under spatial reflections we simulate the cases where the wave-packet approaches the kink from negative or positive spatial infinity. We extract the energy transmission and reflection coefficients as functions of the central frequency of the phonon wave-packet for the different lattice spacings. For large lattice spacings the wave-packet is always fully reflected while for smaller spacing the amount of reflection and transmission depends on the central frequency. We also identify scenarios in which the target kink acquires a non-zero velocity from its interaction with the wave-packet.

nlin.PS↗

arXiv2022

Excited fermions on kinks and the Dirac sea

We study quantum effects of recently discovered kink solitons which are constructed self-consistently by coupling to a single, excited fermion bound state. Our studies are based on the observation that in a semi-classical expansion the energies of this single level and of the Dirac sea should be treated equally. For these kink solutions we compute the energy of the Dirac sea as the fermion vacuum polarization energy. We find it to be substantial and to typically outweigh the energy gain from binding the single level.

hep-th↗

arXiv2021

Chiral Soliton Models and Nucleon Structure Functions

We outline and review the computations of polarized and unpolarized nucleon structure functions within the bosonized Nambu-Jona-Lasinio chiral soliton model. We focus on a consistent regularization prescription for the Dirac sea contribution and present numerical results from that formulation. We also reflect on previous calculations on quark distributions in chiral quark soliton models and attempt to put them into perspective.

hep-ph↗

arXiv2018

Collective Coordinate Methods and Their Applicability to $φ^4$ Models

Collective coordinate methods are frequently applied to study dynamical properties of solitons. These methods simplify the field equations - typically partial differential equations - to ordinary differential equations for selected excitations. More importantly though, collective coordinates provide a practical means to focus on particular modes of otherwise complicated dynamical processes. We review the application of collective coordinate methods in the analysis of the kink-antikink interaction within the $φ^4$ soliton model and illuminate discrepancies between these methods and the exact results from the field equations.

nlin.PS↗

arXiv2002

Casimir Effects in Renormalizable Quantum Field Theories

We review the framework we and our collaborators have developed for the study of one-loop quantum corrections to extended field configurations in renormalizable quantum field theories. We work in the continuum, transforming the standard Casimir sum over modes into a sum over bound states and an integral over scattering states weighted by the density of states. We express the density of states in terms of phase shifts, allowing us to extract divergences by identifying Born approximations to the phase shifts with low order Feynman diagrams. Once isolated in Feynman diagrams, the divergences are canceled against standard counterterms. Thus regulated, the Casimir sum is highly convergent and amenable to numerical computation. Our methods have numerous applications to the theory of solitons, membranes, and quantum field theories in strong external fields or subject to boundary conditions.

hep-th↗

arXiv2001

The Spin of the Nucleon in Effective Models

The three flavor soliton approach for baryons is utilized to discuss effects of flavor symmetry breaking in the baryon wave--functions on axial current matrix elements. The flavor content of the singlet axial current matrix elements, that parameterizes the quark spin contribution to the total angular momentum, is disentangled and studied as a function of the effective flavor symmetry breaking. Here the nucleon and the Lambda--hyperon are considered.

hep-ph↗

arXiv2001

Soliton Models for the Nucleon and Predictions for the Nucleon Spin Structure

In these lectures the three flavor soliton approach for baryons is reviewed. Effects of flavor symmetry breaking in the baryon wave--functions on axial current matrix elements are discussed. A bosonized chiral quark model is considered to outline the computation of spin dependent nucleon structure functions in the soliton picture.

hep-ph↗

arXiv2000

Radial Excitations of low-lying Baryons and the Structure of the Z^+ Penta-QuarK

Within the collective quantization scheme for chiral solitons we discuss states in higher dimensional representations of flavor SU(3) and their relation to radially excited states in the octet. We also consider states which do not have counterparts of the same quantum numbers in the octet or decuplet and cannot be built from three quarks. We focus on the Z^+ penta-quark, presumably the lightest such state, by estimating its mass and decay width.

hep-ph↗

arXiv1999

Hadron Structure Functions in a Chiral Quark Model

We present a consistent regularization procedure for calculating hadron structure functions in a bosonized chiral quark model. We find that the Pauli-Villars regularization scheme is most suitable. We also summarize the phenomenology of structure functions calculated in the valence quark approximation.

hep-ph↗

arXiv1999

Nucleon Structure Functions in a Chiral Soliton Model

The computation of nucleon structure functions within the Nambu-Jona-Lasinio chiral soliton model is outlined. After some technical remarks on the issue of regularization numerical results for the both unpolarized and polarized structure functions are presented. The generalization to flavor SU(3) is sketched.

hep-ph↗

arXiv1998

The parity-violating pion-nucleon coupling constant from a realistic three flavor Skyrme model

We study the parity-violating pion-nucleon coupling $G_π$ in the framework of a realistic three flavor Skryme model. We find a sizeable enhancement of $G_π\simeq 0.8 ... 1.3 \cdot 10^{-7}$ compared to previous calculations in two-flavor models with vector mesons. This strangeness enhancement stems from induced kaon fields of the chiral soliton and the non-monotoneous dependence on symmetry breaking of the nucleon matrix element of the flavor singlet piece of the operator associated with these induced fields. Both features are sensitive to four quark operators including an $\bar s s$ pair.

nucl-th↗

arXiv1998

Hyperons as collective excitations of chiral solitons

According to the large $N_C$ limit of QCD baryons are considered as soliton solutions in effective mesons theories. While the classical solitons dwell in the isospin subgroup of flavor SU(3) hyperon states are generated by canonical quantization of the collective coordinates which describe the flavor orientation of the soliton. The resulting Hamiltonian is diagonalized exactly allowing one to discuss the dependence of various baryon properties on flavor symmetry breaking. In particular axial charges, baryon magnetic moments and radiative decay widths are considered.

hep-ph↗