Related papers: Generalized Galilei-Invariant Classical Mechanics
This is the first in a pair of articles that classify the configuration space and kinematic symmetry groups for $N$ identical particles in one-dimensional traps experiencing Galilean-invariant two-body interactions. These symmetries explain…
The equations for the electromagnetic two-body problem are neutral-delay equations that for generic initial data have solutions with discontinuous derivatives. If one wants to use these neutral-delay equations with arbitrary initial data,…
We consider a generalization of nonrelativistic Schr\"odinger-Higgs Lagrangian by introducing a nonstandard kinetic term. We show that this model is Galilean invariant, we construct the conserved charges associated to the symmetries and…
An open issue in classical relativistic mechanics is the consistent treatment of the dynamics of classical $N$-body systems of mutually-interacting particles. This refers, in particular, to charged particles subject to EM interactions,…
The Newtonian n-Body Problem is modified assuming positive inertial masses but different sign for the interacting force which is assumed with the possibility of two different signs for the gravitational masses, according to the prescription…
Anomalies are renormalization group invariants that constrain the dynamics of quantum field theories. We show that certain anomalies for discrete global symmetries imply that the underlying theory either spontaneously breaks its generalized…
We compute the purely local-in-time (scale-free and logarithm-free) part of the conservative dynamics of gravitationally interacting two-body systems at the fourth post-Minkowskian order, and at the thirtiest order in velocity. The…
This is a brief overview of our work on the theory of group invariant solutions to differential equations. The motivations and applications of this work stem from problems in differential geometry and relativistic field theory. The key…
An explicit dynamical model for non relativistic quantum mechanics with an effective gravitational interaction is proposed, which, as being well defined, allows in principle for the evaluation of every physical quantity. Its non unitary…
As a straightforward generalization and extension of our previous paper, J. Phys. A50 (2017) 215201 we study aspects of the quantum and classical dynamics of a $3$-body system with equal masses, each body with $d$ degrees of freedom, with…
A Lagrangian description of a classical particle in a 9-dimensional flat Finslerian space with a cubic metric function is constructed. The general solution of equations of motion for such a particle is obtained. The Galilean law of inertia…
In this note we approach the classical, Newtonian, gravitational $N$-body problem by mean of a new, original numerical integration method. After a short summary of the fundamental characteristics of the problem, including a sketch of some…
For the gravitational $n$-body problem, the simplest motions are provided by those rigid motions in which each body moves along a Keplerian orbit and the shape of the system is a constant (up to rotations and scalings) configuration…
It is shown that all possible gravitational, gauge and other interactions experienced by particles in ordinary d-dimensions (one-time) can be described in the language of two-time physics in a spacetime with d+2 dimensions. This is obtained…
The equations of motion for $N$ non-relativistic particles attracting according to Newton's law are shown to correspond to the equations for null geodesics in a $(3N+2)$-dimensional Lorentzian, Ricci-flat, spacetime with a covariantly…
In the context of physics didactics, alternative instructional approaches have often been employed to facilitate conceptual understanding of various topics. In this article, an alternative formulation for analyzing the motion of bodies on…
Scale invariance has received very little attention in physics. Nevertheless, it provides a natural conceptual foundation for a relational understanding of the universe, where absolute size loses meaning and only dimensionless ratios retain…
The equations of motion describing all physical systems, except gravity, remain invariant if a constant is added to the Lagrangian. In the conventional approach, gravitational theories break this symmetry exhibited by all other physical…
It is demonstrated that the measured spatial separation of two objects, at rest in some inertial frame, is invariant under space-time transformations. This result holds in both Galilean and Special Relativity. A corollary is that there are…
We provide a complete classification of all abelian gauge invariant $p$-form theories with equations of motion depending only on the second derivative of the field---the $p$-form analogues of the Galileon scalar field theory. We construct…