Related papers: A Toy Model of Renormalization and Reformulation
This presentation includes an introductory discussion of the unification of fundamental forces, properties of the elementary particles, Quantum Electrodynamics, the transition from Quantum Electrodynamics and Weak Interactions to…
Discrete inverse problems correspond to solving a system of equations in a stable way with respect to noise in the data. A typical approach to enforce uniqueness and select a meaningful solution is to introduce a regularizer. While for most…
Inverse problems describe the task of recovering an underlying signal of interest given observables. Typically, the observables are related via some non-linear forward model applied to the underlying unknown signal. Inverting the non-linear…
The paper deals with three evolution problems arising in the physical modelling of acoustic phenomena of small amplitude in a fluid, bounded by a surface of extended reaction. The first one is the widely studied wave equation with acoustic…
In the standard perturbation theory (SPT) of self-gravitating Newtonian fluid in an expanding universe, recurrence relations for higher-order solutions are well known and play an important role both in practical applications and in…
We develop a theoretical approach to ``spontaneous stochasticity'' in classical dynamical systems that are nearly singular and weakly perturbed by noise. This phenomenon is associated to a breakdown in uniqueness of solutions for fixed…
The generalized Langrangian mean theory provides exact equations for general wave-turbulence-mean flow interactions in three dimensions. For practical applications, these equations must be closed by specifying the wave forcing terms. Here…
The intricate machinery of perturbative quantum field theory has largely been devoted to the 'dynamical' side of the theory: simple states are evolved in complicated ways. This article begins to address this lopsided treatment. Although it…
We present a novel technique to obtain relativistic corrections to the central force problem in the Lagrangian formulation, using a generalized potential energy function. We derive a general expression for a generalized potential energy…
In this work, we analyze a Lagrangian formalism recently proposed to approach the issue of the Abraham-Lorentz force. Instead of involving only position and velocity, as usual in Classical Mechanics, this Lagrangian involves the…
We propose a variational regularisation approach for the problem of template-based image reconstruction from indirect, noisy measurements as given, for instance, in X-ray computed tomography. An image is reconstructed from such measurements…
The usual derivation of the Lagrangian of a model for massive vector bosons, by spontaneous symmetry breaking of a gauge theory, implies that the prefactors of the various interaction terms are uniquely determined functions of the coupling…
We study new Legendre transforms in classical mechanics and investigate some of their general properties. The behaviour of the new functions is analyzed under coordinate transformations.When invariance under different kinds of…
The construction of effective Lagrangians commonly involves the application of the `classical equation of motion' to eliminate redundant structures and thus generate the minimal number of independent terms. We investigate this procedure in…
In his monograph \emph{Conjugate Duality and Optimization}, Rockafellar puts forward a ``perturbation + duality'' method to obtain a dual problem for an original minimization problem. First, one embeds the minimization problem into a family…
It is well known that quantum-mechanical perturbation theory often give rise to divergent series that require proper resummation. Here I discuss simple ways in which these divergences can be avoided in the first place. Using the elementary…
Consistent interactions that can be added to a free, Abelian gauge theory comprising a finite collection of BF models and a finite set of two-form gauge fields (with the Lagrangian action written in first-order form as a sum of Abelian…
A simple mathematical procedure is introduced which allows redefining in an exact way divergent integrals and limits that appear in the basic equations of classical electrodynamics with point charges. In this way all divergences are at once…
The equations of motion for electromechanical systems are traced back to the fundamental Lagrangian of particles and electromagnetic fields, via the Darwin Lagrangian. When dissipative forces can be neglected the systems are conservative…
It is argued that, contrary to conventional wisdom, no trustworthy universal self-force/radiative corrections to the Lorentz force equation, can be derived from the basic tenets of classical electrodynamics. This concords with the apparent…