Related papers: On Generalizations of the Minimal Complementary En…
The least action principle is established for the dynamics of a test particle in a dilaton-Maxwell background. These dynamics and background are invariant under the action of the dilatation transformation; explicit form of the corresponding…
In string theory the coupling ``constants'' appearing in the low-energy effective Lagrangian are determined by the vacuum expectation values of some (a priori) massless scalar fields (dilaton, moduli). This naturally leads one to expect a…
A brief review is presented of the stability domain of three- and four-charge ground-states when the constituent masses vary. Rigorous results are presented, based on the scaling behavior and the convexity properties deduced from the…
The theory of freely-propagating massless higher spins is usually formulated via gauge fields and parameters subject to trace constraints. We summarize a proposal allowing to forego them by introducing only a pair of additional fields in…
We establish a Lagrangian variational framework for general relativistic continuum theories that permits the development of the process of Lagrangian reduction by symmetry in the relativistic context. Starting with a continuum version of…
It is shown that geometric optical description of electromagnetic wave with account of its polarization in curved space-time can be obtained straightforwardly from the classical variational principle for electromagnetic field. For this end…
A method for designing variational principles for the dynamics of a possibly dissipative and non-conservatively forced chain of particles is demonstrated. Some qualitative features of the formulation are discussed.
We propose a novel variational principle in electrostatics and show that one can derive mirror equation in the context of image problem starting from this principle. The corresponding Euler-Lagrange equation is seen to lead to Green's…
An approach to the teaching of electromagnetism to senior undergraduate students, designed for overcoming the fragmentation of the theory is described. As usual it starts from the static case, but it is strictly based on Helmholtz theorem…
We consider a discrete model of planar elasticity where the particles, in the reference configuration, sit on a regular triangular lattice and interact through nearest neighbor pairwise potentials, with bonds modeled as linearized elastic…
We determine the electrostatic self-force at rest in an arbitrary static metric with cylindrical symmetry in the linear approximation in the Newtonian constant. In linearised Einstein theory, we express it in terms of the components of the…
We present a systematic derivation of the constraints that the relativity principle imposes between coefficients of a deformed (but rotational invariant) momentum composition law, dispersion relation, and momentum transformation laws, at…
This paper is devoted to classical variational problems for planar elastic curves of clamped endpoints, so-called Euler's elastica problem. We investigate a straightening limit that means enlarging the distance of the endpoints, and obtain…
The variational principle for a spherical configuration consisting of a thin spherical dust shell in gravitational field is constructed. The principle is consistent with the boundary-value problem of the corresponding Euler-Lagrange…
An infinite-range model of an elastic manifold pulled through a random potential by an applied force $F$ is analyzed focusing on inertial effects. When the inertial parameter, $M$, is small, there is a continuous depinning transition from a…
A dual variational principle is defined for the nonlinear system of PDE describing the dynamics of dislocations in elastic solids. The dual variational principle accounting for a specified set of initial and boundary conditions for a…
We propose a new classical approach for describing a system composed of $n$ interacting particles with variable mass connected by a single field with no predefined form ($n$-VMVF systems). Instead of assuming any particular nature or…
We construct the theoretical base for the search of the possible experimental manifestations of the torsion field at low energies. The weakrelativistic approximation to the Dirac equation in an external torsion field is considered. For the…
In materials that undergo martensitic phase transformation, macroscopic loading often leads to the creation and/or rearrangement of elastic domains. This paper considers an example {involving} a single-crystal slab made from two martensite…
Motivated by our earlier work, we show in this paper rigorously that the ground state energy and degeneracy of an infinitely extended system of interacting electrons in the background of a homogeneous magnetic field and two separated…