We discuss stable, overcomplete, non-orthogonal phase-space expansions with respect to generalized coherent states. The key concepts are Weyl-Heisenberg frames and quantitative measures of phase-space localization. On an abstract level, we introduce and investigate the localization of general frames.

The field of charged impurities in narrow band-gap semiconductors and Weyl semimetals can create electronhole pairs when the total charge Ze of the impurity exceeds a value Zce. The particles of one charge escape to infinity, leaving a screening space charge. The result is that the observable dimensionless impurity charge Q∞ is less than Z but greater than Zc. There is a corresponding effect fo...

The evolution of 4-dimensional and (4+d)-dimensional (d=1,2) cosmological models based on the integrable Weyl geometry are considered numerically both for empty space-time and for scalar field with non minimal coupling with gravity.

A theory of non-unitary-invertible as well as unitary canonical transformations is formulated in the context of Weyl's phase space representations. Exact solutions of the transformation kernels and the phase space propagators are given for the three fundamental canonical maps as linear, gauge and contact (point) transformations. Under the nonlinear maps a phase space representation is mapped to...

0.1. In this paper we construct a number of geometrically meaningful 1– and 2– cocycles of infinite dimensional Lie groups and Lie algebras. The groups are groups of diffeomorphisms of smooth manifolds and their subgroups, such as the group of symplectomorphisms of a symplectic manifold; the Lie algebras are algebras of vector fields. Coefficient spaces of the cocycles are spaces of various ten...

It has been suggested recently, based on subtle field-theoretical considerations, that the electromagnetic response of Weyl semimetals and the closely related Weyl insulators can be characterized by an axion term θE·B with space and time dependent axion angle θ(r,t). Here we construct a minimal lattice model of the Weyl medium and study its electromagnetic response by a combination of analytica...

We reconsider the problem of the anomalous Hall effect in ferromagnetic SrRuO3, incorporating insights from the recently developed theory of Weyl semimetals. We demonstrate that SrRuO3 possesses a large number of Weyl nodes, separated in momentum space, in its bandstructure. While the nodes normally do not coincide with the Fermi energy, unless the material is doped, we show that even the nodes...

Weyl fermions that emerge at band crossings in momentum space caused by the spin-orbit interaction act as magnetic monopoles of the Berry curvature and contribute to a variety of novel transport phenomena such as anomalous Hall effect and magnetoresistance. However, their roles in other physical properties remain mostly unexplored. Here, we provide evidence by neutron Brillouin scattering that ...

The Weyl fermion belonging to the real representation of the gauge group provides a simple illustrative example for Lüscher’s gauge-invariant lattice formulation of chiral gauge theories. We can explicitly construct the fermion integration measure globally over the gauge-field configuration space in the arbitrary topological sector; there is no global obstruction corresponding to the Witten ano...

In this paper, we establish Schur-Weyl reciprocity for the q-analogue of the alternating group. We analyze the sign q-permutation representation of the Hecke algebra HQ(q),r(q) on the rth tensor product of Z2-graded Q-vector space V = V0⊗V1 in detail, and examine its restriction to the qanalogue of the alternating group H1Q(q),r(q). In consequence, we find out that if dimV0 = dimV1, then the ce...