Related papers: Gauge Functions in Classical Mechanics: From Undri…
By using the multipolar gauge it is shown that the quantum mechanics of an electrically charged particle moving in a prescribed classical electromagnetic field (wave mechanics) may be expressed in a manner that is gauge invariant, except…
The fallacies associated with the gauge concept in electromagnetism are illustrated. A clearer and more valid formulation of the basics of classical electromagnetism is provided by recognizing existing physical constraints as well as the…
We derive the path integral action for a particle moving in three dimensional fuzzy space. From this we extract the classical equations of motion. These equations have rather surprising and unconventional features: They predict a cut-off in…
We derive both Lagrangian and Hamiltonian mechanics as gauge theories of Newtonian mechanics. Systematic development of the distinct symmetries of dynamics and measurement suggest that gauge theory may be motivated as a reconciliation of…
A survey of topics of recent interest in Hamiltonian and Lagrangian dynamical systems, including accessible discussions of regularization of the central force problem; inequivalent Lagrangians and Hamiltonians; constants of central force…
The gap between classical mechanics and quantum mechanics has an important interpretive implication: the Universe must have an irreducible fundamental level, which determines the properties of matter at higher levels of organization. We…
Positing complex adaptive systems made of agents with relations between them that can be composed, it follows that they can be described by gauge theories similar to elementary particle theory and general relativity. By definition, a…
Differentiable physics provides a new approach for modeling and understanding the physical systems by pairing the new technology of differentiable programming with classical numerical methods for physical simulation. We survey the rapidly…
The structure of classical electrodynamics based on the variational principle together with causality and space-time homogeneity is analyzed. It is proved that in this case the 4-potentials are defined uniquely. On the other hand, the…
We study new Legendre transforms in classical mechanics and investigate some of their general properties. The behaviour of the new functions is analyzed under coordinate transformations.When invariance under different kinds of…
In this paper of "The Epistemology of Contemporary Physics" series we investigate the epistemological significance and sensibility (and hence interpretability and interpretation) of classical mechanics in its Newtonian and non-Newtonian…
The reasons which restrict opportunities of classical mechanics at the description of nonequilibrium systems are discussed. The way of overcoming of the key restrictions is offered. This way is based on an opportunity of representation of…
After revealing difficulties of the standard time-dependent perturbation theory in quantum mechanics mainly from the viewpoint of practical calculation, we propose a new quasi-canonical perturbation theory. In the new theory, the dynamics…
Absolute space is eliminated from the body of mechanics by gauging translations and rotations in the Lagrangian of a classical system. The procedure implies the addition of compensating terms to the kinetic energy, in such a way that the…
The Physics Education Group at the University of Washington is examining the extent to which students are able to use graphs of potential energy vs. position to infer kinematic and dynamic quantities for a system. The findings indicate that…
The relationship between the Hamiltonian and Lagrangean functions in analytical mechanics is a type of duality. The two functions, while distinct, are both descriptive functions encoding the behavior of the same dynamical system. One…
Electromagnetism, the strong and the weak interaction are commonly formulated as gauge theories in a Lagrangian description. In this paper we present an alternative formal derivation of U(1)-gauge theory in a manifestly covariant Hamilton…
If we admit that quantum mechanics (QM) is universal theory, then QM should contain also some description of classical mechanical systems. The presented text contains description of two different ways how the mathematical description of…
Using Grassmann variant of classical mechanics, we construct Lagrangian dynamics of classical spinning particle in (possibly non-abelian) gauge fields. Quantization of this model is briefly discussed.
Some of the important non-classical aspects of quantum mechanics can be described in more intuitive terms if they are reformulated in a geometrical picture based on an extension of the classical phase space. This contribution presents…