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H. Weigel

Publications and source records attributed to H. Weigel.

At least 37 records · Page 2Linked to original sources
arXiv2016

Cosmic Strings Stabilized by Quantum Fluctuations

We compute fermion quantum corrections to the energy of cosmic strings. A number of rather technical tools is needed to formulate this correction and we employ isospin and gauge invariance to verify consistency of these tools. These corrections must also be included when computing the energy of strings that are charged by populating fermion bound states in its background. We find that charged strings are dynamically stabilized in theories similar to the standard model of particle physics.

hep-th↗
arXiv2016

Isospin Invariance and the Vacuum Polarization Energy of Cosmic Strings

We corroborate the previously applied spectral approach to compute the vacuum polarization energy of string configurations in models similar to the standard model of particle physics. The central observation underlying this corroboration is the existence of a particular global isospin transformation of the string configuration. Under this transformation the single particle energies of the quantum fluctuations are invariant, while the inevitable implementation of regularization and renormalization requires operations that are not invariant. We verify numerically that all such variances eventually cancel, and that the vacuum polarization energy obtained in the spectral approach is indeed gauge invariant.

hep-th↗
arXiv2015

Heavy baryons with Strangeness in Soliton Models

We present some recent results from soliton model calculations for the spectrum of baryons with a single heavy quark.The model comprises chiral symmetry for light flavors and (approximate) heavy spin-flavor symmetry for the heavy quarks. We focus on flavor symmetry breaking for strangeness degrees of freedom.

hep-ph↗
arXiv2015

Heavy Baryons with Strangeness in a Soliton Model

We present results from a chiral soliton model calculation for the spectrum of baryons with a single heavy quark (charm or bottom) and non-zero strangeness. We treat the strange components within a three flavor collective coordinate quantization of the soliton that fully accounts for light flavor symmetry breaking. Heavy baryons emerge by binding a heavy meson to the soliton. The dynamics of this heavy meson is described by the heavy quark effective theory with finite mass effects included.

hep-ph↗
arXiv2015

Quantum Stabilization of Cosmic Strings

In the standard model, stabilization of a classically unstable cosmic string may occur through the quantum fluctuations of a heavy fermion doublet. We review numerical results from a semiclassical expansion in a reduced version of the standard model. In this expansion the leading quantum corrections emerge at one loop level for many internal degrees of freedom. The resulting vacuum polarization energy and the binding energy of occupied fermion energy levels are of the same order, and must therefore be treated on equal footing. Populating these bound states lowers the total energy compared to the same number of free fermions. Charged strings are already stabilized for a fermion mass only somewhat larger than the top quark mass. Though obtained in a reduced version these results suggest that neither extraordinarily large fermion masses nor unrealistic couplings are required to bind a cosmic string in the standard model. Furthermore we also review results for a quantum stabilization mechanism that prevents closed Nielsen-Olesen type strings from collapsing.

hep-th↗
arXiv2014

On the Casimir Energy of Frequency Dependent Interactions

Vacuum polarization (or Casimir) energies can be straightforwardly computed from scattering data for static field configurations whose interactions with the fluctuating field are frequency independent. In effective theories, however,such interactions are typically frequency dependent. As a consequence, the relationship between scattering data and the Green's function is modified, which may or may not induce additional contributions to the vacuum polarization energy. We discuss several examples that naturally include frequency dependent interactions: (i) scalar electrodynamics with a static background potential, (ii) an effective theory that emerges from integrating out a heavy degree of freedom, and (iii) quantum electrodynamics coupled to a frequency dependent dielectric material. In the latter case, we argue that introducing dissipation as required by the Kramers-Kronig relations requires the consideration of the Casimir energy within a statistical mechanics formalism, while in the absence of dissipation we can work entirely within field theory, using an alternative formulation of the energy density.

hep-th↗
arXiv2013

Attractive Electromagnetic Casimir Stress on a Spherical Dielectric Shell

Based on calculations involving an idealized boundary condition, it has long been assumed that the stress on a spherical conducting shell is repulsive. We use the more realistic case of a Drude dielectric to show that the stress is attractive, matching the generic behavior of Casimir forces in electromagnetism. We trace the discrepancy between these two cases to interactions between the electromagnetic quantum fluctuations and the dielectric material.

hep-th↗
arXiv2013

Quantum Stabilization of a Closed Nielsen-Olesen String

We revisit the classical instability of closed strings in the Abelian Higgs model. The instability is expressed by a vanishing energy as the torus-like configuration shrinks to zero size. We treat the radius of the torus as a collective coordinate and demonstrate that a quantum mechanical treatment of this coordinate leads to a stabilization of the closed string at small radii.

hep-th↗
arXiv2012

The vacuum nature of the QCD condensates

Recently it was claimed that QCD condensates were associated with the internal dynamics of the hadrons. We challenge this "in-hadron" picture of the QCD condensates and show that it conflicts well established concepts and experimental facts for the example of the quark condensate. We explicitly demonstrate the vacuum nature of the quark condensate by a model calculation.

hep-ph↗
arXiv2011

Cosmic Strings Stabilized by Fermion Fluctuations

We provide a thorough exposition of recent results on the quantum stabilization of cosmic strings. Stabilization occurs through the coupling to a heavy fermion doublet in a reduced version of the standard model. The study combines the vacuum polarization energy of fermion zero-point fluctuations and the binding energy of occupied energy levels, which are of the same order in a semi-classical expansion. Populating these bound states assigns a charge to the string. Strings carrying fermion charge become stable if the Higgs and gauge fields are coupled to a fermion that is less than twice as heavy as the top quark. The vacuum remains stable in the model, because neutral strings are not energetically favored. These findings suggest that extraordinarily large fermion masses or unrealistic couplings are not required to bind a cosmic string in the standard model.

hep-th↗
arXiv2011

Wave-Packet Scattering off the Kink-Solution

We investigate the propagation of a wave--packet in the $ϕ^4$ model. We solve the time-dependent equation of motion for two distinct initial conditions: The wave-packet in a trivial vacuum background and in the background of the kink soliton solution. We extract the scattering matrix from the wave-packet in the kink background at very late times and compare it with the result from static potential scattering in the small amplitude approximation. We vary the size of the initial wave-packet to identify non-linear effects as, for example, the replacement of the center of the kink.

nlin.PS↗
arXiv2011

Fermion Energies in the Background of a Cosmic String

We provide a thorough exposition, including technical and numerical details, of previously published results on the quantum stabilization of cosmic strings. Stabilization occurs through the coupling to a heavy fermion doublet in a reduced version of the standard model. We combine the vacuum polarization energy of fermion zero-point fluctuations and the binding energy of occupied energy levels, which are of the same order in a semi-classical expansion. Populating these bound states assigns a charge to the string. We show that strings carrying fermion charge become stable if the electro-weak bosons are coupled to a fermion that is less than twice as heavy as the top quark. The vacuum remains stable in our model, because neutral strings are not energetically favored. These findings suggests that extraordinarily large fermion masses or unrealistic couplings are not required to bind a cosmic string in the standard model.

hep-th↗
arXiv2011

Stable charged cosmic strings

We study the quantum stabilization of a cosmic string by a heavy fermion doublet in a reduced version of the standard model. We show that charged strings, obtained by populating fermionic bound state levels, become stable if the electro--weak bosons are coupled to a fermion that is less than twice as heavy as the top quark. This result suggests that extraordinarily large fermion masses or unrealistic couplings are not required to bind a cosmic string in the standard model. Numerically we find the most favorable string profile to be a simple "trough" in the Higgs vev of radius $\approx 10^{-18}\,\mathrm{m}$. The vacuum remains stable in our model, because neutral strings are not energetically favored.

hep-th↗
arXiv2010

Gauge Invariance and Vacuum Energies of Non-Abelian String-Configurations

We improve on a method to compute the fermion contribution to the vacuum polarization energy of string-like configurations in a non-Abelian gauge theory. We establish the new method by numerically verifying the invariance under (a subset of) local gauge transformations. This also provides further support for the use of spectral methods to compute vacuum polarization energies in general. We confirm that the vacuum energy in the MS-bar renormalization scheme is tiny as compared to the mass of the fluctuating fermion field. Numerical results for the physical on-shell scheme are also presented.

hep-th↗
arXiv2010

Vacuum Energies of Non--Abelian String--Configurations in 3+1 Dimensions

We develop a method to compute the fermion contribution to the vacuum polarization energy of string--like configurations in a non--abelian gauge theory. This calculation has been hampered previously by a number of technical obstacles. We use gauge invariance of the energy and separation of length scales in the energy density to overcome these obstacles. We present a proof-of-principle investigation that shows that this energy is small in the MS-bar renormalization scheme. The generalization to other schemes is straightforward.

hep-th↗
arXiv2008

On the Decay of Soliton Excitations

In field theory the scattering about spatially extended objects, such as solitons, is commonly described by small amplitude fluctuations. Since soliton configurations often break internal symmetries, excitations exist that arise from quantizing the modes that are introduced to restore these symmetries. These modes represent collective distortions and cannot be treated as small amplitude fluctuations. Here we present a method to embrace their contribution to the scattering matrix. In essence this allows us to compute the decay widths of such collective excitations. As an example we consider the Skyrme model for baryons and explain that the method helps to solve the long--standing Yukawa problem in chiral soliton models.

hep-th↗
arXiv2007

Quantum stabilization of Z-strings, a status report on D=3+1 dimensions

We investigate an extension to the phase shift formalism for calculating one-loop determinants. This extension is motivated by requirements of the computation of Z-string quantum energies in D=3+1 dimensions. A subtlety that seems to imply that the vacuum polarization diagram in this formalism is (erroneously) finite is thoroughly investigated.

hep-th↗