Related papers: Spinning Particles, Braid Groups and Solitons
For non-abelian simple objects in a unitary modular category, the density of their braid group representations, the #P-hard evaluation of their associated link invariants, and the BQP-completeness of their anyonic quantum computing models…
Spin is commonly thought to reflect the true quantum nature of microphysics. We show that spin is related to intrinsic and field-like properties of single particles. These properties change continuously in external magnetic fields.…
It is well known that spinors on oriented Riemannian manifolds cannot be defined as sections of a vector bundle associated with the frame bundle. For this reason spin and spin^c structures are often introduced. In this paper we prove that…
We prove that braid group representations associated to braided fusion categories and mapping class group representations associated to modular fusion categories are always semisimple. The proof relies on the theory of extensions in…
The relativistic wave equation for spin-1/2 particles in the interior Schwarzschild solution in the presence of a uniform magnetic field is obtained. The fully relativistic regime is considered, and the energy levels occupied by the…
We study the problem of determining the isomorphism classes of the virtually cyclic subgroups of the n-string braid groups B_n(S^2) of the 2-sphere S^2. If n is odd, or if n is even and sufficiently large, we obtain the complete…
In this paper we study a quadratic Poisson algebra structure on the space of bilinear forms on $C^{N}$ with the property that for any $n,m\in N$ such that $n m =N$, the restriction of the Poisson algebra to the space of bilinear forms with…
We study the geometric properties of a $2m$-dimensional complex manifold $\mathcal{M}$ admitting a holomorphic reduction of the frame bundle to the structure group $P \subset \mathrm{Spin}(2m,\mathbb{C})$, the stabiliser of the line spanned…
It is generally believed that dispersive polarimetric detection of collective angular momentum in large atomic spin systems gives rise to: squeezing in the measured observable, anti-squeezing in a conjugate observable, and collective spin…
We study the motion of a charged quantum particle, constrained on the surface of a cylinder, in the presence of a radial magnetic field. When the spin of the particle is neglected, the system essentially reduces to an infinite family of…
We consider a 5-dimensional model with geometry ${\cal M} = {\cal M}_4 \times {\cal S}_1$, with compactification radius $R$. The Standard Model particles are localized onto a brane located at y=0, with identical branes localized at…
Symmetry groups are projectively represented in quantum mechanics, and crystalline symmetries are fundamental in condensed matter physics. Here, we systematically present a unified theory of quantum mechanical space groups from two…
A general relation between the Moyal formalisms for a spin and a particle is established. Once the formalism has been set up for a spin, the phase-space description of a particle is obtained from the `contraction' of the group of rotations…
This paper concerns the quantisation of a rigid body in the framework of ``covariant quantum mechanics'' on a curved spacetime with absolute time. The basic idea is to consider the multi-configuration space, i.e. the configuration space for…
The partition algebras are algebras of diagrams (which contain the group algebra of the symmetric group and the Brauer algebra) such that the multiplication is given by a combinatorial rule and such that the structure constants of the…
This paper gives a combinatorial description of spin and spin^c-structures on triangulated PL-manifolds of arbitrary dimension. These formulations of spin and spin^c-structures are established primarily for the purpose of aiding in…
Massive spinning particle in $6d$-Minkowski space is described as a mechanical system with the configuration space $R^{5,1} \times CP^3$. The action functional of the model is unambiguously determined by the requirement of identical…
We construct the U(N) spinning particle theories, which describe particles moving on Kahler spaces. These particles have the same relation to the N=2 string as usual spinning particles have to the NSR string. We find the restrictions on the…
In this manuscript we study the confinement of bosonic and spinning test particles in smooth Randall-Sundrum models. For this, we show that it is possible to find an effective potential which describe the motion of the particle over the…
We construct an algorithm for computing the cycle classes of the spin components of a stratum of differentials in the moduli space of stable curves $\overline{\mathcal{M}}_{g,n}$. In addition, we implement it within the Sage package…