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...
In this talk, I will discuss a subclass of gauged nonlinear sigma models with gauge group U(1) and a general Kaehler target. At critical coupling, such models admit topological soliton solutions called BPS vortices, which solve a system of first order PDEs called the Bogomolny equations. They attain a topological lower energy bound characterized by the degree of a holomorphic map. The most...
We present novel integrable (3+1)-dimensional generalizations for the following (2+1)-dimensional integrable systems: dispersionless BKP, dispersionless asymmetric Nizhnik--Veselov--Novikov, dispersionless Gardner, and dispersionless modified KP equations, and the generalized Benney system. All these new (3+1)-dimensional integrable systems are found using our general construction for a large...
To be determined
We derive an infinite family of time-dependent integral relations by performing weighted integrations of the stress-energy conservation equation in classical field theory. These relations connect weighted spatial integrals of the stress tensor to the second time derivative of weighted averages of the energy density. When this quantity vanishes, as in stationary configurations, or even only at...
We investigate the local dynamics of a class of (p)-dimensional nonlinear rational difference equation systems with power-type nonlinearities, extending several previously studied low-dimensional models to a general higher-dimensional setting. The analysis focuses on the boundedness of solutions and the local asymptotic stability of equilibrium states. By establishing explicit sufficient...
An introductory lecture to the sphaleron in the Electroweak model
Collective coordinate models reduce field dynamics to a few variables, but their accuracy depends strongly on the ansatz. I will discuss a sequence of examples in which the kink profile is adapted to the local geometry or to spatially and temporally varying coefficients. Starting with radial $\phi^4$ kinks in a Schwarzschild-like geometry, I will show how a metric dependent rescaling combined...
Isorotating solitons in (2+1)-dimensional CP^2 nonlinear sigma model with a stabilizing potential term were studied. Families of U(1)×U(1) symmetric solutions with topological degrees equal or larger than 1 are found, which have two angular frequencies and are labeled by two (one topological and the other nontopological) winding numbers k1 ≥ k2. The distributions of the corresponding shear...
We study a resonant system that describes the interaction between long and short waves.
The system is related to a Sasa–Satsuma-type equation and is obtained by a dimensional reduction of a higher-dimensional model;
we also show how it arises within a weakly nonlinear description of wave propagation.
Our main focus is on the soliton solutions and their characteristic behavior. Besides...
We construct gauged linear sigma models whose strong gauge coupling limit yields nonlinear sigma models on Kahler C-space. We derive vortex solutions and their moduli space in the gauged linear sigma models.
Topologically nontrivial solitons often exhibit characteristic fermionic spectra when coupled to Dirac fermions. In many fermion–soliton systems, spectral flow reflects the underlying topology of the soliton. However, it remains unclear which fermion–soliton couplings support this correspondence. In this talk, we approach this problem by analytically investigating several representative...
Q-balls are non-topological solitons that are supposed to have emerged in the early era of our universe via the Affleck-Dine mechanism. During the long cosmological evolution, at some period the vacuum drastically may change, like those in the phase transitions. For such environmental shifts on Q-balls, we introduce the concept of "quench" dynamics, which is governed by the change of the...
A fermionic many-body system with a current mass can be localized within a finite spatial region solely by gravity [1]. Previous studies have investigated systems incorporating electromagnetic fields [2] and their extensions to multiple-shell configurations [3]. In this work, we formulate an Einstein–Dirac–Maxwell system incorporating a Nambu–Jona-Lasinio (NJL)-type four-fermion interaction....
n some theories, defects are metastable and can decay via the nucleation of defects of lower dimensionality through quantum or thermal fluctuations. While at low temperatures the decay is dominated through quantum tunnelling, at higher temperatures thermal decay dominates. Using numerical methods, we simulate defects in a thermal bath at various temperatures and study their thermal decay. In...