Related papers: Extended Particles and the Exterior Calculus
We consider the system of particles on a finite interval with pair-wise nearest neighbours interaction and external force. This model was introduced by Malyshev to study the flow of charged particles on a rigorous mathematical level. It is…
We proceed from the fact that the classical paths of irreducible massive spinning particle lie on a circular cylinder with the time-like axis in Minkowski space. Assuming that all the classical paths on the cylinder are gauge-equivalent, we…
These notes arose from a mini lecture series the author gave at the Early Career Researchers Workshop on Geometric Analysis and PDEs, held in January 2020 at the Matrix institute of the University of Melbourne. We discussed some classical…
In this paper we formulate the theory of nonlinear elasticity in a geometrically intrinsic manner using exterior calculus and bundle-valued differential forms. We represent kinematics variables, such as velocity and rate-of-strain, as…
Theories of physics can be considered viable if the initial value problem and the energy conditions are formulated self-consistently. The former allow a uniquely determined dynamical evolution of the system, and the latter guarantee that…
The results on the initial boundary value problem for Einstein's vacuum field equation obtained in \cite{friedrich:nagy} rely on an unusual gauge. One of the defining gauge source functions represents the mean extrinsic curvature of the…
When applied to a dipole source subjected to acceleration which is violent and long lasting (``extreme acceleration''), Maxwell's equations predict radiative power which augments Larmor's classical radiation formula by a nontrivial amount.…
A general Hamiltonian theory for the adiabatic motion of relativistic charged particles confined by slowly-varying background electromagnetic fields is presented based on a unified Lie-transform perturbation analysis in extended phase space…
One hundred years ago this year attempts began to generalise general relativity with the ambition of incorporating electromagnetism alongside gravitation in a unified field theory. These developments led to gauge theories and models with…
The first-principles formulation of quantum mechanics relevant for quantum chemistry and trapped quantum gases involves particles in the continuous space $\mathbb R^d$. We present a unified framework and modular algorithm for learning…
We present a novel derivation of both the Minkowski metric and Lorentz transformations from the consistent quantification of a causally ordered set of events with respect to an embedded observer. Unlike past derivations, which have relied…
Extended Theories of Gravity can be considered a new paradigm to cure shortcomings of General Relativity at infrared and ultraviolet scales. They are an approach that, by preserving the undoubtedly positive results of Einstein's Theory, is…
The notion of inertial reference frame is abandoned and I replaced it by a local reference frame on which the fundamental law of mechanics is expressed. The distant interactions of cause and effect are modeled by the propagation of waves…
We propose an extended structural dynamics framework that enriches classical mechanics by treating particle orientation and internal structure as fundamental phase-space coordinates. This extension preserves Hamiltonian structure and…
Causal variational principles, which are the analytic core of the physical theory of causal fermion systems, are found to have an underlying Hamiltonian structure, giving a formulation of the dynamics in terms of physical fields in…
We present an introduction to the study of a relativistic particle moving under the influence of its own Frenet-Serret curvatures. With the aim of introducing the notation and conventions used in this paper, we first recall the action of a…
We derive an effective Hamiltonian for a quantum system constrained to a submanifold (the constraint manifold) of configuration space (the ambient space) by an infinite restoring force. We pay special attention to how this Hamiltonian…
This paper is devoted to the analysis of random motions on the line and in the space R^d (d > 1) performed at finite velocity and governed by a non-homogeneous Poisson process with rate \lambda(t). The explicit distributions p(x,t) of the…
Recently, classical results on completeness of trajectories of Hamiltonian systems obtained at the beginning of the seventies, have been revisited, improved and applied to Lorentzian Geometry. Our aim here is threefold: to give explicit…
The multiplicative Newton-like method developed by the author et al. is extended to the situation where the dynamics is restricted to the orthogonal group. A general framework is constructed without specifying the cost function. Though the…