Related papers: Progress in Classical and Quantum Variational Prin…
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…
In mechanics, common energy principles are based on fixed boundary conditions. However, in bridge engineering structures, it is usually necessary to adjust the boundary conditions to make the structure's internal force reasonable and save…
We show the convergence of the solutions to the massive nonlinear Klein-Gordon equation toward solutions to a relativistic Euler with potential type system in the semi-classical limit. In particular, the momentum and the density of…
Non-relativistic quantum mechanics for a free particle is shown to emerge from classical mechanics through an invariance principle under transformations that preserve the Heisenberg position-momentum inequality. These transformations are…
The Bohr-van Leeuwen theorem is often summarized as saying that there is no classical magnetic susceptibility, in particular no diamagnetism. This is seriously misleading. The theorem assumes position dependent interactions but this is not…
By using a formal analogy between statistical mechanics of mean field spin systems and analytical mechanics of viscous liquids -at first pointed out by Francesco Guerra, then recently developed by the authors- we give the thermodynamic…
The energy and time variables of the elementary classical dynamical systems are described geometrically, as canonically conjugate coordinates of an extended phase-space. It is shown that the Galilei action of the inertial equivalence group…
The Hamilton principle is a variation principle describing the isolated and conservative systems, its Lagrange function is the difference between kinetic energy and potential energy. By Feynman path integration, we can obtain the Hermitian…
The general, non-dissipative, two-fluid model in plasma physics is Hamiltonian, but this property is sometimes lost or obscured in the process of deriving simplified (or reduced) two-fluid or one-fluid models from the two-fluid equations of…
The principle of correspondence (or classical limit) is essential in quantum mechanics. Yet, how and why quantum phenomena vanish at the macroscopic scale are issues still open to debate. Here, quantum mechanical predictions for…
In Elementary Cycles theory elementary quantum particles are consistently described as the manifestation of ultra-fast relativistic spacetime cyclic dynamics, classical in the essence. The peculiar relativistic geometrodynamics of…
It is first shown that when the Schr\"{o}dinger equation for a wave function is written in the polar form, complete information about the system's {\em quantum-ness} is separated out in a single term $Q$, the so called `quantum potential'.…
Minimizing the Action integral of a Lagrangian provides the Euler-Lagrange equation of motion in the elegant machinery of Lagrangian Mechanics. However two relations define the divergence of current and energy-momentum, and provide an…
In this work, we follow the idea of the De Broglie's matter waves and the analogous method that Schr\"{o}dinger founded wave equation, but we apply the more essential Hamilton principle instead of the minimum action principle of Jacobi…
The usual Heisenberg uncertainty relation for position and momentum may be replaced by an exact equality, for suitably chosen measures of position and momentum uncertainty. This "exact" uncertainty relation is valid for_all_ pure states,…
We prove a Noether type symmetry theorem to fractional problems of the calculus of variations with classical and Riemann-Liouville derivatives. As result, we obtain constants of motion (in the classical sense) that are valid along the mixed…
Quantization of energy balance equations, which describe a separatrix -- like motion is presented. The method is based on an exact canonical transformation of the energy--time pair to the action-angle canonical pair, $ (E,t)\to (I,\theta)…
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…
The Generalized Uncertainty Principle and the related minimum length are normally considered in non-relativistic Quantum Mechanics. Extending it to relativistic theories is important for having a Lorentz invariant minimum length and for…
Conventional scattering theory is incomplete in that it does not adequately describe the behaviour of the wave function at macroscopic distances from the scattering reaction volume. In scattering experiments particles are incident from…