Related papers: Exploring the action landscape with trial world-li…
Many quantization schemes rely on analogs of classical mechanics where the connections with classical mechanics are indirect. In this work I propose a new and direct connection between classical mechanics and quantum mechanics where the…
We discuss the action principle and resulting Hamiltonian equations of motion for a class of integer-valued cellular automata introduced recently [1]. Employing sampling theory, these deterministic finite-difference equations are mapped…
Extremal principles can generally be divided into two rather distinct classes. There are, on the one hand side, formulations based on the Lagrangian or Hamiltonian mechanics, respectively, dealing with time dependent problems, but…
In this paper, we extend the \emph{principle of least action} and show that a \emph{Lagrange density} always exists for the usual linear pde or linear fractional problems $\oA\,u=f$ in physics, if the usual causality conditions $u|_{t<0}=0$…
The principle of stationary action is a cornerstone of modern physics, providing a powerful framework for investigating dynamical systems found in classical mechanics through to quantum field theory. However, computational neuroscience,…
We introduce an action principle for a class of integer valued cellular automata and obtain Hamiltonian equations of motion. Employing sampling theory, these discrete deterministic equations are invertibly mapped on continuum equations for…
We study the action for a non-Abelian charged particle in a non-Abelian background field in the worldline formalism, described by real bosonic variables, leading to the well known equations given by Wong. The isospin parts in the action can…
Action-dependent field theories are systems where the Lagrangian or Hamiltonian depends on new variables that encode the action. They model a larger class of field theories, including non-conservative behavior, while maintaining a…
This paper provides a new admissibility criterion for choosing physically relevant weak solutions of the equations of Lagrangian and continuum mechanics when non-uniqueness of solutions to the initial value problem occurs. The criterion is…
Recently, there has been an increasing interest in modelling and computation of physical systems with neural networks. Hamiltonian systems are an elegant and compact formalism in classical mechanics, where the dynamics is fully determined…
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…
Nature provides a way to understand physics with reinforcement learning since nature favors the economical way for an object to propagate. In the case of classical mechanics, nature favors the object to move along the path according to the…
Relativistic action-at-a-distance theories with interactions that propagate at the speed of light in vacuum are investigated. We consider the most general action depending on the velocities and relative positions of the particles. The…
We consider a classical field theory whose equations of motion follow from the least action principle, but the class of admissible trajectories is restricted by differential equations. The key element of the proposed construction is the…
In Hamiltonian mechanics the equations of motion may be considered as a condition on the tangent vectors to the solution; they should be null-vectors of the symplictic structure. Usually the formalism for the field case is done by replacing…
An action having an acceleration term in addition to the usual velocity term is analyzed. The quantum mechanical system is directly defined for Euclidean time using the path integral. The Euclidean Hamiltonian is shown to yield the…
Starting from the Dirac equation in external electromagnetic and torsion fields we derive a path integral representation for the corresponding propagator. An effective action, which appears in the representation, is interpreted as a…
The derivation of the recently proposed nonlinear quantum evolution of gravity from an action principle is considered in this brief note. It is shown to be possible if a set of consistency conditions are satisfied that are analogous to the…
It has been known for a long time that Einstein's field equations when projected onto a black hole horizon looks very similar to a Navier-Stokes equation in suitable variables. More recently, it was shown that the projection of Einstein's…
Machine Learning algorithms are typically regarded as appropriate optimization schemes for minimizing risk functions that are constructed on the training set, which conveys statistical flavor to the corresponding learning problem. When the…