Related papers: Magnetic point groups and space groups
In this article we prove some previously announced results about metric ultraproducts of finite simple groups. We show that any non-discrete metric ultraproduct of alternating or special linear groups is a geodesic metric space. For more…
Some special solutions of the Einstein-Maxwell action with a non-negative cosmological constant and a very heavy point mass particle have been obtained. The solutions correspond to static spacetime of locally constant curvature in its…
Magneto-inertial range dominated by magnetic helicity has been studied using results of numerical simulations, laboratory measurements, solar, solar wind, the Earth's and planets' magnetosphere observations (spacecraft measurements), and…
This paper addresses the three following questions. (i) How the structures of group and of chain of groups enter nuclear, atomic and molecular spectroscopy? (ii) How these structures can be exploited, in a quantum- mechanical framework, in…
We consider a category whose morphisms are bordisms of $n$-dimensional pseudomanifolds equipped with a certain additional structure (coloring). On the other hand, we consider the product $G$ of $(n+1)$ copies of infinite symmetric group. We…
We describe isomorphisms of groups of several periodic infinite matrices and isomorphisms of groups of invertible elements of unital locally matrix algebras.
This book offers to study locally compact groups from the point of view of appropriate metrics that can be defined on them, in other words to study "Infinite groups as geometric objects", as Gromov writes it in the title of a famous…
We describe recent links between two topics: geometric structures on manifolds in the sense of Ehresmann and Thurston, and dynamics "at infinity" for representations of discrete groups into Lie groups.
We present an overview of the subject of Magnetic Particles, starting at a level suitable for advanced high-school students and ending at a level suitable for current practitioners in the field. The sub-topics covered include: Types of…
Symmetry is fundamental to understanding our physical world. An antisymmetry operation switches between two different states of a trait, such as two time-states, position-states, charge-states, spin-states, chemical-species etc. This review…
The concepts of symmetry and its breakdown are investigated in two different terms according to whether the resulting asymmetry is universal or only obtained for a special configuration: we shall illustrate this by considering in the first…
We use the mathematical structure of group algebras and $H^{+}$-algebras for describing certain problems concerning the quantum dynamics of systems of angular momenta, including also the spin systems. The underlying groups are ${\rm SU}(2)$…
We analyze the classical equations of motion for a particle moving in the presence of a static magnetic field applied in the $ z $ direction, which varies as $ {1\over{x^2}} $. We find the symmetries through Lie's method of group analysis.…
A hidden gauge theory structure of quantum mechanics which is invisible in its conventional formulation is uncovered. Quantum mechanics is shown to be equivalent to a certain Yang-Mills theory with an infinite-dimensional gauge group and a…
We briefly review the distinction between abstract groups and symmetry groups of objects, and discuss the question of which groups have appeared as the symmetry groups of physical objects. To our knowledge, the quaternion group (a beautiful…
In supersymmetry the anomalous magnetic moment of particles belonging to the same supermultiplet is related by simple sum rules. We study the modification of these sum rules in the case of spontaneously broken N=1 global supersymmetry.
A group-category is an additively semisimple category with a monoidal product structure in which the simple objects are invertible. For example in the category of representations of a group, 1-dimensional representations are the invertible…
In this paper, starting from pure group-theoretical point of view, we develop a regular approach to describing particles with different spins in the framework of a theory of scalar fields on the Poincare group. Such fields can be considered…
The irreducible representations of all of the 80 diperiodic groups, being the symmetries of the systems translationally periodical in two directions, are calculated. To this end, each of these groups is factorized as the product of a…
We study massive and massless conical defects in Minkowski and de Sitter spaces in various spacetime dimensions. The energy-momentum of a defect, considered as an (extended) relativistic object, is completely characterized by the holonomy…