Related papers: What can Physics learn from Continuum Mechanics ?
We give a short outline, in Sec.\ 2, of the historical development of the gauge idea as applied to internal ($U(1),\, SU(2),\dots$) and external ($R^4,\,SO(1,3),\dots$) symmetries and stress the fundamental importance of the corresponding…
Quantum mechanics is a theory that is as effective as it is counterintuitive. While quantum practices operate impeccably, they compel us to embrace enigmatic phenomena like the collapse of the state vector and non-locality, thereby pushing…
The physics of complex systems stands to greatly benefit from the qualitative changes in data availability and advances in data-driven computational methods. Many of these systems can be represented by interacting degrees of freedom on…
Teleparallel gravity has significantly increased in popularity in recent decades, bringing attention to Einstein's other theory of gravity. In this Review, we relate this form of geometry to the broader metric-affine approach to forming…
Some examples of three-dimensional metrics of constant curvature defined by solutions of nonlinear integrable differential equations and their generalizations are constructed. The properties of Riemann extensions of the metrics of constant…
Quantum mechanics, one of the most successful theories in the history of science, was created to account for physical systems not describable by classical physics. Though it is consistent with all experiments conducted thus far, many of its…
The teleparallel formulation of gravity theories reveals close structural analogies to electrodynamics, which are more hidden in their usual formulation in terms of the curvature of spacetime. We show how every locally Lorentz invariant…
It is shown that nonlinear electrodynamics of the Born--Infeld theory type may be exploited to shed insight into a few fundamental problems in theoretical physics, including rendering electromagnetic asymmetry to energetically exclude…
The limits of linear electrodynamics are reviewed, and possible directions of nonlinear extension are explored. The central theme is that the qualitative character of the empirical successes of quantum electrodynamics must be used as a…
An overview is given of the current status of the theory and observations of the acceleration of the expansion of the observable part of the Universe. Contents 1. Historical Introduction 2. Friedmann equations and cosmological acceleration…
1. Connection between integration and differentiation/ Gauss theorem. Coordinate-free definitions: gradient, divergence, curl. Stokes theorem. 2. Elements of continuum mechanics/ Continuity equation. Stress tensor. Euler equation.…
Despite the importance of non-equilibrium statistical mechanics in modern physics and related fields, the topic is often omitted from undergraduate and core-graduate curricula. Key aspects of non-equilibrium physics, however, can be…
String theory has transformed our understanding of geometry, topology and spacetime. Thus, for this special issue of Foundations of Physics commemorating "Forty Years of String Theory", it seems appropriate to step back and ask what we do…
We develop a theory to represent dislocated single crystals at the mesoscopic scale by considering concentrated effects, governed by the distribution theory combined with multiple-valued kinematic fields. Our approach gives a new…
We describe some instances of the appearance of Chern's mathematical ideas in physics. By means of simple examples, we bring out the geometric and topological ideas which have found application in describing the physical world. These…
The general theory of (nonlinear) partial differential equations originated by S. Lie had a significant development in the past 30-40 years. Now this theory has solid foundations, a proper language, proper techniques and problems, and a…
Long sequences of successive direct (projective) measurements or observations of a few "uninteresting" physical quantities of a quantum system may reveal indirect, but precise and unambiguous information on the values of some very…
Quintessence theories for cosmic acceleration imbue dark energy with a non-trivial dynamics that offers hope in distinguishing the physical origin of the component. We review quintessence models with an emphasis on this dynamics and discuss…
Riemannian and teleparallel geometrical approaches to the investigation of Maxwell electrodynamics shown that a unified field theory of gravitation and electromagnetism a la Einstein can be obtained from a stationary metric. This idea…
A continuum model to study the influence of dislocations on the electronic properties of condensed matter systems is described and analyzed. The model is based on a geometrical formalism that associates a density of dislocations with the…