Related papers: Nonlinear realizations, the orbit method and Kohn'…
Given a symmetry group one can construct the invariant dynamics using the technique of nonlinear realizations or the orbit method. The relationship between these methods is discussed. Few examples are presented.
Some aspects of phase transitions can be more conveniently studied in the orbit space of the action of the symmetry group. After a brief review of the fundamental ideas of this approach, I shall concentrate on the mathematical aspect and…
The method of nonlinear realizations is applied for the conformally invariant description of the spinning particles in terms of geometrical quantities of the parameter spaces of the one dimensional N - extended superconformal groups. We…
In these lectures we review two approaches to constructing particle actions from coset spaces of symmetry groups: non-linear realisations and coadjoint orbits. At the level of particle actions, we observe that they coincide. We also provide…
In this paper we classify in terms of Lie point symmetries the three-dimensional nonrelativistic motion of charged particles in arbitrary time-independent electromagnetic fields. The classification is made on the ground of equivalence…
Single particle dynamics in electron microscopes, ion or electron lithographic instruments, particle accelerators, and particle spectrographs is described by weakly nonlinear ordinary differential equations. Therefore, the linear part of…
A symmetry analysis is presented for the three-dimensional nonrelativistic motion of charged particles in arbitrary stationary electromagnetic fields. The general form of the Lie point symmetries is found along with the fields that respect…
We present the applications of methods from nonlinear local harmonic analysis in variational framework to calculations of nonlinear motions in polynomial/rational approximations (up to any order) of arbitrary n-pole fields. Our approach is…
We construct the systems of the harmonic and Pais-Uhlenbeck oscillators, which are invariant with respect to arbitrary noncompact Lie algebras. The equations of motion of these systems can be obtained with the help of the formalism of…
The coadjoint orbit method is applied to the construction of Hamiltonian dynamics of massless particles of arbitrary helicity. The unusual transformation properties of canonical variables are interpreted in terms of nonlinear realizations…
We use group theoretic methods to obtain the extended Lie point symmetries of the quantum dynamics of a scalar particle probing the near horizon structure of a black hole. Symmetries of the classical equations of motion for a charged…
A new approach to relativistic mechanics is proposed, suitable to describe dynamics of different kinds of relativistic particles. Mathematically it is based on an application of the recent geometric theory of nonholonomic systems on fibred…
The method of nonlinear realizations is applied to construct new dynamical realizations of the Lifshitz group in mechanics, hydrodynamics, and field theory.
The classical problem of attitude stability in a central gravity field is generalized to that on a stationary orbit around a uniformly-rotating asteroid. This generalized problem is studied in the framework of geometric mechanics. Based on…
Inhomogeneous quantum cosmology is modeled as a dynamical system of discrete patches, whose interacting many-body equations can be mapped to a non-linear minisuperspace equation by methods analogous to Bose-Einstein condensation.…
We consider some nonlinear elliptic equations on ${\mathbb R}^n$ and ${\mathbb S}^n$. By the method of moving spheres, we obtain the symmetry properties of solutions and some nonexistence results. Moreover, by the global bifurcation theory,…
The orbital motion is derived for a non-spinning test-mass in the relativistic, gravitational field of a rotationally deformed body not restricted to the equatorial plane or spherical orbit. The gravitational field of the central body is…
Application of nonlinear symmetry realisation technique to gravity is studied. We identify the simplest extensions of the Poincare group suitable for nonlinear realisation. Among them only one model is suitable for description of massless…
The equations of motion for a fully ionized hydrogenic plasma in applied coaxial electric and magnetic fields are analyzed, where the term for the Hall effect in the generalized Ohm's law equation picks up a factor of 1/2 relative to its…
We consider a $(1+N)$-body problem in which one particle has mass $m_0 \gg 1$ and the remaining $N$ have unitary mass. We can assume that the body with larger mass (central body) is at rest at the origin, coinciding with the center of mass…