Related papers: On the space-time Monopole equation

The introduction of a space-time lattice as a regulator of field theories breaks symmetries associated with continuous space-time, i.e.\ Poincar{\'e} invariance and supersymmetry. A non-zero gluino mass in the supersymmetric Yang-Mills…

Time-dependent soliton solutions are explicitly derived in a five-dimensional theory endowed with one (warped) extra-dimension. Some of the obtained geometries, everywhere well defined and technically regular, smoothly interpolate between…

This is the third part of a four-paper sequence, which establishes the Threshold Conjecture and the Soliton-Bubbling vs.~Scattering Dichotomy for the energy critical hyperbolic Yang--Mills equation in the $(4+1)$-dimensional Minkowski…

Motivated by the work of P.L. Lions and J-C. Rochet [12], concerning multi-time Hamilton-Jacobi equations, we introduce the theory of multi-time systems of conservation laws. We show the existence and uniqueness of solution to the Cauchy…

This doctoral work deals with the analysis of some Yang-Mills solutions on 4-dimensional de Sitter space d$S_4$. The conformal equivalence of this space with a finite Lorentzian cylinder over the 3-sphere and also with parts of Minkowski…

Non-commutative differential geometry allows a scalar field to be regarded as a gauge connection, albeit on a discrete space. We explain how the underlying gauge principle corresponds to the independence of physics on the choice of vacuum…

Using new approach to construction of space-times emerging from quantum information theory, we identify the space of quantum states that generates the Schwarzschild space-time. No quantisation procedure is used. The emergent space-time is…

Two different scenarios (light-front and equal-time) are possible for Yang-Mills theories in two dimensions. The exact $\bar q q$-potential can be derived in perturbation theory starting from the light-front vacuum, but requires essential…

The solutions of the Bogomolny equation in anti-de Sitter space-time are obtained by using Darboux transformations with both constant spectral parameters and variable "spectral parameters". These solutions give the Yang-Mills-Higgs fields…

We study the theory of scattering for a Schr"odinger equation in an external time dependent magnetic field in the Coulomb gauge, in space dimension 3. The magnetic vector potential is assumed to satisfy decay properties in time that are…

The unitary S-matrix for the space-time non-commutative QED is constructed using the $\star$-time ordering which is needed in the presence of derivative interactions. Based on this S-matrix, perturbation theory is formulated and Feynman…

This study investigates the possibility of a homogeneous and isotropic cosmological solution within the context of the Maxwell-Weyl gauge theory of gravity. To achieve this, we utilize the Einstein-Yang-Mills theory as an analogy and…

We recast the quaternionic Gursey-Tze solution, which is a fourfold quasi-periodic self-dual Yang-Mills field with a unit instanton number per Euclidean spacetime cell, into an ordinary coordinate formulation. After performing the sum in…

We give a definition of gauge-invariant magnetic monopoles in Yang-Mills theory without using the Abelian projection due to 't Hooft. They automatically appear from the Wilson loop operator. This is shown by rewriting the Wilson loop…

The $N=4$ supersymmetric self-dual Yang-Mills theory in a four- dimensional space with signature $(2,2)$ is formulated in harmonic superspace. The on-shell constraints of the theory are reformulated in the equivalent form of vanishing…

We demonstrate that the five vortex equations recently introduced by Manton ariseas symmetry reductions of the anti-self-dual Yang--Mills equations in four dimensions. In particular the Jackiw--Pi vortex and the Ambj\o rn--Olesen vortex…

In this work, we develop a space--time Chebyshev spectral collocation method for three-dimensional Maxwell's equations and combine it with tensor-network techniques in Tensor-Train (TT) format. Under constant material parameters, the…

Scaling behavior in the moduli space of monopole and dyon solutions in the Einstein-Yang-Mills theory in the asymptotically anti-de Sitter space is derived. The mass of monopoles and dyons scales with respect to their magnetic and electric…

This paper is concerned with the Cauchy problem of the $2$D Zakharov-Kuznetsov equation. We prove bilinear estimates which imply local in time well-posedness in the Sobolev space $H^s({\mathbb{R}}^2)$ for $s > -1/4$, and these are optimal…

We prove boundedness and inverse logarithmic decay in time of solutions to the Teukolsky equations on Schwarzschild-Anti-de Sitter backgrounds with standard boundary conditions originating from fixing the conformal class of the non-linear…