Related papers: Spin and the Symplectic Flag Manifold
Spectroscopic measurements with low-temperature scanning tunneling microscopes have been used very successfully for studying not only individual atomic or molecular spins on surfaces but also complexly designed coupled systems. The symmetry…
Let $\Gamma$ be a finite graph and let $\Gamma_n$ be the "$n$th cone over $\Gamma$" (i.e., the join of $\Gamma$ and the complete graph $K_n$). We study the asymptotic structure of the chip-firing group $\text{Pic}^0(\Gamma_n)$.
In recent work, we initiated a research program aimed at the systematic investigation of quantum superintegrable systems describing the interaction of two non-relativistic spin-$1/2$ particles in three-dimensional Euclidean space. In that…
We realize every closed flat 3-manifold as a cusp section of a complete, finite-volume hyperbolic 4-manifold whose symmetry group acts transitively on the set of cusps. Moreover, for every such 3-manifold, a dense subset of its flat metrics…
Known symmetry groups are insufficient to describe the various couplings among spin, charge, and spatial degrees of freedom in fermionic systems. To address this problem, we introduce spin-charge groups (SCGs), which provide a unified…
A system of two particles with spin s=0 and s=1/2 respectively, moving in a plane is considered. It is shown that such a system with a nontrivial spin-orbit interaction can allow an 8 dimensional Lie algebra of first-order integrals of…
The spin of supersymmetric particles can be determined at $e^+e^-$ colliders unambiguously. This is demonstrated for a characteristic set of non-colored supersymmetric particles -- smuons, selectrons, and charginos/neutralinos. The analysis…
We construct, for each convex polytope, possibly nonrational and nonsimple, a family of compact spaces that are stratified by quasifolds, i.e. each of these spaces is a collection of quasifolds glued together in an suitable way. A quasifold…
We investigate continuous transitive actions of semitopological groups on spaces, as well as separately continuous transitive actions of topological groups.
We study the orbit structure and the geometric quantization of a pair of mutually commuting hamiltonian actions on a symplectic manifold. If the pair of actions fulfils a symplectic Howe condition, we show that there is a canonical…
Recently, Cohen and Glashow pointed out that all known experimental tests of relativistic kinematics are consistent with invariance of physics under the four-parameter subgroup Sim(2) of the Lorentz group. The massive one-particle…
Symplectic unitary representations for the Poincar\'{e} group are studied. The formalism is based on the noncommutative structure of the star-product, and using group theory approach as a guide, a consistent physical theory in phase space…
General topologically invariant microscopical expressions for quantum numbers of particle-like solitons ("skyrmions") are derived for a class of (2+1)D models. Skyrmions are either half-integer spin fermions with odd electric charge or…
We address the problem of computing the fundamental group of a symplectic $S^1$-manifold for non-Hamiltonian actions on compact manifolds, and for Hamiltonian actions on non-compact manifolds with a proper moment map. We generalize known…
The main result of this paper is a new parameterization of the orbits of a symmetric subgroup on a partial flag variety. The parameterization is in terms of certain Spaltenstein varieties, on one hand, and certain nilpotent orbits, on the…
We consider a connected symplectic manifold $M$ acted on by a connected Lie group $G$ in a Hamiltonian fashion. If $G$ is compact, we prove give an Equivalence Theorem for the symplectic manifolds whose squared moment map $\parallel \mu…
We rewrite the standard 4-dimensional Dirac equation in terms of quaternionic 2-component spinors, leading to a formalism which treats both massive and massless particles on an equal footing. The resulting unified description has the…
The largest allowed symmetry in a spin-1 quantum system is an $SU(3)$ symmetry rather than the $SO(3)$ spin rotation. In this work, we reveal some $SU(2)$ symmetries as subgroups of $SU(3)$ that, to the best of our knowledge, have not…
Quantum tomography for continuous variables is based on the symplectic transformation group acting in the phase space. A particular case of symplectic tomography is optical tomography related to the action of a special orthogonal group. In…
A group action is called polar if there exists an immersed submanifold (a section) which intersects all orbits orthogonally. Such group actions have been studied extensively on symmetric spaces. We show how to construct a manifold admitting…