Related papers: Pauli-Villars Regularization in a Discrete Light-C…
The (2+1) dimensional gauged O(3) nonlinear sigma model with Chern-Simons term is canonically quantized. Furthermore, we study a nonminimal coupling in this model implemented by means of a Pauli-type term. It is shown that the set of…
We present a relativistic formulation of pion loop corrections to the coupling of photons with nucleons on the light-front. Vertex and wave function renormalization constants are computed to lowest order in the pion field, including their…
We study the ray transform $L$ over null (light) rays in the pseudo-Euclidean space with signature $(n',n'')$, $n'\ge2$, $n''\ge2$. We analyze the normal operator $L'L$, derive an inversion formula, and prove stability estimates. We show…
We apply convex regularization techniques to the problem of calibrating the local volatility surface model of Dupire taking into account the practical requirement of discrete grids and noisy data. Such requirements are the consequence of…
Stable light bullets and clusters of them are presented in the monostable regime using the mean-field Lugiato-Lefever equation [Gopalakrishnan, Panajotov, Taki, and Tlidi, Phys. Rev. Lett. 126, 153902 (2021)]. It is shown that…
We examine in detail nonperturbative corrections for low lying energies of a symmetric triple-well potential with non-equivalent vacua, for which there have been disagreement about asymptotic formulas and controversy over the validity of…
Adaptive cubic regularization methods have emerged as a credible alternative to linesearch and trust-region for smooth nonconvex optimization, with optimal complexity amongst second-order methods. Here we consider a general/new class of…
We present a family of non-local variational regularization methods for solving tomographic problems, where the solutions are functions with range in a closed subset of the Euclidean space, for example if the solution only attains values in…
We present results for the first two moments of the light-cone distribution amplitudes of the pion and kaon pseudo-scalar mesons and of the rho, K* and phi vector mesons. The calculations are performed on the RBC/UKQCD collaborations'…
We investigate the principal chiral model between two and four dimensions by means of a non perturbative Wilson-like renormalization group equation. We are thus able to follow the evolution of the effective coupling constants within this…
This paper explores a fully discrete approximation for a nonlinear hyperbolic PDE-constrained optimization problem (P) with applications in acoustic full waveform inversion. The optimization problem is primarily complicated by the…
We present a discretisation of the 3+1 formulation of the Yang-Mills equations in the temporal gauge, using a Lie algebra-valued extension of the discrete de Rham (DDR) sequence, that preserves the non-linear constraint exactly. In contrast…
Light-cone quantization of gauge field theory is considered. With a careful treatment of the relevant degrees of freedom and where they must be initialized, the results obtained in equal-time quantization are recovered, in particular the…
Several convergence results in Hilbert scales under different source conditions are proved and orders of convergence and optimal orders of convergence are derived. Also, relations between those source conditions are proved. The concept of a…
3 pages presentation of the theory of discrete conformal parameterization using circle patterns or its linearized theory. Principal results and ideas.
In this article, we develop and present a novel regularization scheme for ill-posed inverse problems governed by nonlinear time-dependent partial differential equations (PDEs). In our recent work, we introduced a bi-level regularization…
Using the method of separation of variables, we developed a vector nonparaxial theory for the nonlinear wave equations in strong field approximation. We found that exact localized vortex soliton solution exists for the nonlinear 3D+1 vector…
Perturbative Coulomb gauge Yang-Mills theory within the first order formalism is considered. Using a differential equation technique and dimensional regularization, analytic results for both the ultraviolet divergent and finite parts of the…
We consider perturbed nonlinear ill-posed equations in Hilbert spaces, with operators that are monotone on a given closed convex subset. A simple stable approach is Lavrentiev regularization, but existence of solutions of the regularized…
A simple theory for the leading-order correction g_1(r) to the structure of a hard-sphere liquid with discrete (e.g. square-well) potential perturbations is proposed. The theory makes use of a general approximation that effectively…