Related papers: Spinning Particles, Braid Groups and Solitons
Partition functions for M2-brane theories in various backgrounds are computed. We consider in particular configurations of membranes at orbifold singularities preserving N=5 or N=6 supersymmetry. The worldvolume membrane theory for some of…
$\mathbb{Z}_d$ Parafermions are exotic non-Abelian quasiparticles generalizing Majorana fermions, which correspond to the case $d=2$. In contrast to Majorana fermions, braiding of parafermions with $d>2$ allows to perform an entangling…
In this paper we represent the generalization of relativistic quantum mechanics on the base of eght-component values "octons", generating associative noncommutative spatial algebra. It is shown that the octonic second-order equation for the…
A model-independent formulation of anyons as spinning particles is presented. The general properties of the classical theory of (2+1)-dimensional relativistic fractional spin particles and some properties of their quantum theory are…
We discuss the group theory relevant to the ground-state baryons in large N_c QCD. For very large representation, the group generators become classical variables. We find the form of the classical generators for the completely symmetric N…
We factorize the space-time coordinates of Minkowski space into Weyl spinors with components in a split Clifford algebra. Poisson brackets are defined for spinor-valued canonical variables and applied to the quantization of point particles…
In this paper we present simplifying techniques which allow one to compute the quiver diagrams for various D-branes at (non-Abelian) orbifold singularities with and without discrete torsion. The main idea behind the construction is to take…
Unitary braiding operators can be used as robust entangling quantum gates. We introduce a solution-generating technique to solve the $(d,m,l)$-generalized Yang-Baxter equation, for $m/2\leq l \leq m$, which allows to systematically…
We examine the problem of determining which representations of the braid group on a Riemann surface are carried by the wave function of a quantized Abelian Chern-Simons theory interacting with non-dynamical matter. We generalize the…
Quantum spin rings represent fundamental model systems that exhibit distinctive quantum phenomena-such as quantum critical behavior and quasiparticle excitations-arising from their periodic boundary conditions and enhanced quantum…
In this article we study the space of positive scalar curvature metrics on totally nonspin manifolds with spin boundary. We prove that for such manifolds of certain dimensions, those spaces are not connected and have nontrivial fundamental…
We consider the universal family $E_n^d$ of superelliptic curves: each curve $\Sigma_n^d$ in the family is a $d$-fold covering of the unit disk, totally ramified over a set $P$ of $n$ distinct points; $\Sigma_n^d\hookrightarrow E_n^d\to…
Let $(\mathrm{U},\mathrm{U}^\imath)$ be the quantum symmetric pair of arbitrary finite type and $G^*$ be the associated dual Poisson-Lie group. Generalizing the work of De Concini and Procesi, the first author introduced an integral form…
Let $LG$ be the loop group of a compact, connected Lie group $G$. We show that the tangent bundle of any proper Hamiltonian $LG$-space $\mathcal{M}$ has a natural completion $\overline{T}\mathcal{M}$ to a strongly symplectic…
Given a smooth partial action $\alpha$ of a Lie groupoid $G$ on a smooth manifold $M,$ we provide necessary and sufficient conditions for $\alpha$ to be globalizable with smooth globalization. As an application, we provide results on the…
We obtain general bounds on scattering processes involving charged particles in 1+1 spacetime dimensions. After a general analysis we derive mostly numerical bounds on couplings in theories with $O(N)$ and $U(N)$ global symmetries. The…
A generalized Chan-Paton construction is presented which is analogous to the tensor product of vector bundles. To this end open string theories are considered where the space of states decomposes into sectors whose product is described by a…
In this paper we define a new family of groups which generalize the {\it classical braid groups on} $\C $. We denote this family by $\{B_n^m\}_{n \ge m+1}$ where $n,m \in \N$. The family $\{ B_n^1 \}_{n \in \N}$ is the set of classical…
We investigate classical integrable spins defined on the reduced phase spaces of coadjoint orbits of $G= SU(N)$ and study quantum mechanics of them. After discussions on a complete set of commuting functions on each orbit and construction…
In two spatial dimensions, spin characterizes how particle states re-phase under changes of frame that leave their momentum and energy invariant. Massless particles can in principle have non-trivial spin in this sense, but all existing…