Related papers: The octonionic phase space Hopf map
We introduce three area preserving maps with phase space structures which resemble circle packings. Each mapping is derived from a kicked Hamiltonian system with one of three different phase space geometries (planar, hyperbolic or…
Hopf terms are topological theta terms that are associated with a host of interesting physics, including anyons, statistical transmutation, chiral edge states, and the spin quantum Hall effect. Here, we show that Hopf terms can appear in…
The structure and the dynamics of massless higher spin fields in various dimensions are reviewed with an emphasis on conformally invariant higher spin fields. We show that in D=3,4,6 and 10 dimensional space-time the conformal higher spin…
The orbit space of an octupole, a traceless symmetric third-rank tensor of $SO(3)$, is shown to be a three-dimensional body with three cusps and two cuspidal edges. It is demonstrated that for a unique choice of orbit space coordinates its…
We consider the generalized (10+10)-dimensional D=4 quantum phase spaces containing translational and Lorentz spin sectors associated with the dual pair of twist-quantized Poincare Hopf algebra $\mathbb{H}$ and quantum Poincare Hopf group…
We deal here with the geometry of the twistor fibration $\mathcal{Z} \to \bb{S}^3_1$ over the De Sitter 3-space. The total space $\mathcal{Z}$ is a five dimensional reductive homogeneous space with two canonical invariant almost CR…
The twistor space of representations on an open variety maps to a weight two space of local monodromy transformations around a divisor component at infinty. The space of $\sigma$-invariant sections of this slope-two bundle over the twistor…
It is shown that there exists a twistor space on the $n$-fold connected sum of complex projective planes $n\mathbb{CP}^2$, whose algebraic dimension is one and whose general fiber of the algebraic reduction is birational to an elliptic…
The fermionic fields of one generation of the Standard Model, including the Lorentz spinor degrees of freedom, can be identified with components of a single real 64-dimensional semi-spinor representation S of the group Spin(11,3). We…
The aim of the present paper is the investigation of $Spin(9)$-structures on 16-dimensional manifolds from the point of view of topology as well as holonomy theory. First we construct several examples. Then we study the necessary…
It is known that a two-dimensional spin system can acquire a topological Hopf term by coupling to massless Dirac fermions whose energy spectrum has a single cone. But it is challenging to realize the Hopf term in condensed matter physics…
We consider a field theory with target space being the two dimensional sphere S^2 and defined on the space-time S^3 x R. The Lagrangean is the square of the pull-back of the area form on S^2. It is invariant under the conformal group…
The Hopf index equates the multiplicity of a zero of a section of a vector bundle with a winding number. We give eight analogues for isotropic sections of bundles with quadratic form. There are applications to cosection localised virtual…
We describe explicitly the algebra of Spin(9)-invariant, translation-invariant, continuous valuations on the octonionic plane. Namely, we present a basis in terms of invariant differential forms and determine the Bernig-Fu convolution on…
We show that band topology can dramatically change the photophysics of two-dimensional (2D) semiconductors. For systems in which states near the band extrema are of multiple orbitals character and the spinors describing the orbital…
We describe a diagram containing the zero sets of the moment maps associated to the diagonal U(1) and Sp(1) actions on the quaternionic projective space HP^n. These sets are related both to focal sets of submanifolds and to…
We construct two-band topological semimetals in four dimensions using the unstable homotopy of maps from the three-torus $T^3$ (Brillouin zone of a 3D crystal) to the two-sphere $S^2$. Dubbed ``Hopf semimetals'', these gapless phases…
We study a quantum version of the SU(2) Hopf fibration $S^7 \to S^4$ and its associated twistor geometry. Our quantum sphere $S^7_q$ arises as the unit sphere inside a q-deformed quaternion space $\mathbb{H}^2_q$. The resulting four-sphere…
We determine the Hofer-Zehnder capacity for twisted tangent bundles over closed surfaces for (i) arbitrary constant magnetic fields on the two-sphere and (ii) strong constant magnetic fields for higher genus surfaces. On $S^2$ we further…
We study the topology of the space of harmonic maps from $S^2$ to \CP 2$. We prove that the subspaces consisting of maps of a fixed degree and energy are path connected. By a result of Guest and Ohnita it follows that the same is true for…