Related papers: The Crystallographic Spin Point Groups and their R…
We derive manifestly covariant actions of spinning particles starting from coadjoint orbits of isometry groups, by using Hamiltonian reductions. We show that the defining conditions of a classical Lie group can be treated as Hamiltonian…
The theory of particle scattering is concerned with transition amplitudes between states that belong to unitary representations of the Poincar\'e group. The latter acts as the isometry group of Minkowski spacetime $\mathbb{M}$, making…
Collective rotations are common in active matter, enhancing cohesion, transport, and mixing. They are typically attributed to chiral non-reciprocal dynamics due to intrinsic particle chirality, torque-generating interactions among units, or…
We consider indecomposable representations of the Klein four group over a field of characteristic $2$ and of a cyclic group of order $pm$ with $p,m$ coprime over a field of characteristic $p$. For each representation we explicitly describe…
Spiral spin liquids are unique classical spin liquids that occur in many frustrated spin systems, but do not comprise a new phase of matter. Owing to extensive classical ground-state degeneracy, the spins in a spiral spin liquid thermally…
We develop general techniques for computing the fundamental group of the configuration space of $n$ identical particles, possessing a generic internal structure, moving on a manifold $M$. This group generalizes the $n$-string braid group of…
The scalar spin chirality (SSC), defined as a triple product of spins, is essential for describing noncoplanar spin structures and understanding chiral physics in magnetic systems. Traditionally, SSC has been discussed primarily in the…
We relate the linear asymptotic representation theory of the symmetric groups to its spin counterpart. In particular, we give explicit formulas which express the normalized irreducible spin characters evaluated on a strict partition $\xi$…
We present a systematic classification of emergent particles in all 528 magnetic layer groups and 394 magnetic rod groups, which describe two-dimensional and one-dimensional crystals respectively. Our approach is via constructing a…
This article aims at giving a general presentation of spintronics, an important field of research developing today along many new directions in physics of condensed matter. We tried to present simply the physical phenomena involved in…
Group theoretical methods are used to determine the electromagnetic properties of artificial magnetic meta-materials, based solely upon the symmetries of the underlying constituent particles. Point groups for such materials are determined.…
The finite orbits of the braid group action on Stokes matrices are studied and are shown to be the orbits on ordered sets of reflections, generating finite groups. All invariants of a reflection arrangement are determined. Determination of…
We perform the computations necessary to establish a multiplicity one statement for the irreducible representations of a finite spin group which in turn yields the classification of irreducible representations of finite spin groups. (The…
One of the main obstacles that prevents practical applications of antiferromagnets is the difficulty of manipulating the magnetic order parameter. Recently, following the theoretical prediction [J. \v{Z}elezn\'y et al., PRL 113, 157201…
Materials with interesting physical properties are often designed based on our understanding of the target physical effects. The physical properties can be either explicitly observed ("apparent") or concealed by the perceived symmetry…
The general form of the operators commuting with the ground representation (appearing in many physical problems within single particle approximation) of the group is found. With help of the modified group projector technique, this result is…
Symmetry provides important insight in understanding the nature of phase transitions. In the presence of crystalline symmetries, new phenomena in phase transition can emerge, such as intertwined orders and emergent symmetries. In this work,…
Skyrmions are important in topological quantum field theory for being soliton solutions of a nonlinear sigma model and in information technology for their attractive applications. Skyrmions are believed to be circular and stripy spin…
The phenomenological theory of the flexomagnetoelectric coupling in crystals of the cubic, tetragonal and orthorhombic crystal systems has been suggested. Secondary role of the crystal structure chirality was shown. Oppositely, significant…
In this paper we complete the classification of spin manifolds admitting parallel spinors, in terms of the Riemannian holonomy groups. More precisely, we show that on a given n-dimensional Riemannian manifold, spin structures with parallel…