Stability estimate for the broken non-abelian X-ray transform in Minkowski space

Solitary waves and vortices in non-Abelian gauge theories with matter

We consider a non-Abelian gauge theory in R^{4} equipped with the Minkowski metric, which provides a model for the interaction between a bosonic matter field and a gauge field with gauge group SU(2). We prove the existence of solitary waves which are related to those found for the Klein-Gordon-Maxwell equations.

Three dimensional vortices in Abelian Gauge Theories

In this paper we consider an Abelian Gauge Theory in R^4 equipped with the Minkowski metric. This theory leads to a system of equations, the Klein-Gordon-Maxwell equations, which provide models for the interaction between the electromagnetic field and matter. A three dimensional vortex is a finite energy solution of these equations in which the magnetic field looks like the field created by a finite solenoid. Under suitable assumptions, we prove the existence of vortex-solutions.

高固定频率下联络的高斯光束与反问题

Gaussian beams and inverse problems for connections at high fixed frequency

本文利用射流丛语言构造高斯光束，从高固定频率 DN 映射恢复边界信息，证明非阿贝尔 X 射线变换单射时联络可规范等价恢复，并由三次非线性 DN 映射恢复始终单射的破损非阿贝尔 X 射线变换。

Hylomorphic Vortices in Abelian Gauge Theories

We consider an Abelian Gauge Theory in R4 equipped with the Minkowski metric. This theory leads to a system of equations, the Klein-Gordon- Maxwell equations, which provide models for the interaction between the electromagnetic field and matter. We assume that the nonlinear term is such that the energy functional is positive; this fact makes the theory more suitable for physical models. A three dimensional vortex is a finite energy, stationary solution of these equations such that the matter field has nontrivial angular momen- tum and the magnetic field looks like the field created by a finite…

从主动局部测量中反演 Minkowski 空间中的 Yang–Mills–Higgs 场

Retrieving Yang--Mills--Higgs fields in Minkowski space from active local measurements

本文利用源到解数据，在 Standard Model 满足的非退化条件下，通过 Lie 代数中心的 abelian 分量与波的非线性相互作用，从 Minkowski 空间中的 Yang–Mills–Higgs 方程反演 Yang–Mills 势和 Higgs 场（精确到规范）。

Doubly Periodic Self-Dual Vortices for a Relativistic Non-Abelian Chern--Simons Model

In this paper we establish a multiplicity result concerning the existence of doubly periodic solutions for a $2\times2$ nonlinear elliptic system arising in the study of self-dual non-Abelian Chern--Simons vortices. We show that the given system admits at least two solutions when the Chern--Simons coupling parameter $κ>0$ is sufficiently small; while no solutions exist for $κ>0$ sufficiently large. As in [36] we use a variational formulation of the problem. Thus, we obtain a first solution via a (local) minimization method and show that it is asymptotically gauge-equivalent to the (broken) pri…