Related papers: Noether's Theorem and its Complement: A Gateway to…
We investigate a kinetic model for interacting particles whose masses are integer multiples of an elementary mass. These particles undergo binary collisions which preserve momentum and energy but during which some number of elementary…
Elementary Cycles Theory is a self-consistent, unified formulation of quantum and relativistic physics. Here we introduce its basic quantum aspects. On one hand, Newton's law of inertia states that every isolated particle has persistent…
We begin by presenting the classical deterministic problems of the calculus of variations, with emphasis on the necessary optimality conditions of Euler-Lagrange and the Noether theorem. As examples of application, we obtain the…
The energy-momentum conservation laws for general reduced-fluid (e.g., gyrofluid) models are derived by Noether method from a general reduced variational principle. The reduced canonical energy-momentum tensor (which is explicitly…
A generalized uncertainty principle is obtained from a conformally transformed action containing a scalar field and a unique constraint. The constraint's Lagrange multiplier is found to obey a relativistic diffusion equation transforming…
Why is gauge symmetry so important in modern physics, given that one must eliminate it when interpreting what the theory represents? In this paper we discuss the sense in which gauge symmetry can be fruitfully applied to constrain the space…
A two-time quantum theory of a system of two particles with the direct electromagnetic interaction based on a quantum version of the action principle is considered. An analog of Schrodinger equation for the system is obtained.
We consider Noether symmetries within Hamiltonian setting as transformations that preserve Poincar\'e-Cartan form, i.e., as symmetries of characteristic line bundles of nondegenerate 1-forms. In the case when the Poincar\'e-Cartan form is…
Non-autonomous non-relativistic mechanics is formulated as Lagrangian and Hamiltonian theory on fibre bundles over the time axis R. Hamiltonian mechanics herewith can be reformulated as particular Lagrangian theory on a momentum phase…
A self-action problem for a pointlike charged particle arbitrarily moving in flat spacetime of three dimensions is considered. Outgoing waves carry energy-momentum and angular momentum; the radiation removes energy and angular momentum from…
Particles and fields are standard components in numerical simulations like transport simulations in nuclear physics and have very well understood dynamics. Still, a common problem is the interaction between particles and fields due to their…
This paper analyzes, for a multi-particle system of spin-1/2 particles, the consequences of replacing the Poincare group as fundamental symmetry group by the de Sitter group SO(3,2). The flat-space approximation of the de Sitter group by…
Modified versions of the Schr\"{o}dinger equation have been proposed in order to incorporate the description of measurement processes into the mathematical structure of quantum theory. Typically, these proposals introduce new physical…
We present a general algorithm constructing a discretization of a classical field theory from a Lagrangian. We prove a new discrete Noether theorem relating symmetries to conservation laws and an energy conservation theorem not based on any…
The approach to a substantiation of thermodynamics is offered. A conservative system of interacting elements, which is not in equilibrium, is used as a model. This system is then split into small subsystems that are accepted as being in…
We develop a formulation of particle mechanics in which the functional relation between force and kinetic energy is derived directly from local conservation mechanical energy $E$, rather than postulated through Newton's second law or a…
The result of a numerical simulation of two interacting particles in the framework of Nonunitary Newtonian Gravity is presented here. Particles are held close together by a 3-d harmonic trap and interact with each other via an `electrical'…
The goal of this article is to investigate the dynamics of semi-relativistic or non-relativistic charged particles in interaction with a scalar meson field. Our main contribution is the derivation of the classical dynamics of a…
The law of action-reaction, considered by Ernst Mach the cornerstone of physics, is thoroughly used to derive the conservation laws of linear and angular momentum. However, the conflict between momentum conservation law and Newton's third…
The motion of a system of particles under electromagnetic interaction is considered. Under the assumption that the force acting on an electric charge is given by the sum of the electromagnetic fields produced by any other charged particles…