We compute the Weyl anomaly for an abelian Wilson surface by using a regularization that respects the gauge invariance. We then study the loop space on which lives a one-form connection. We restrict ourselves to the subsector consisting of only concentrical circular loops, and derive a Maxwell type action on this restricted loop space.

We show that the Schrödinger equation in phase space proposed by Torres-Vega and Frederick is canonical in the sense that it is a natural consequence of the extended Weyl calculus obtained by letting the Heisenberg group act on functions (or half-densities) defined on phase space. This allows us, in passing, to solve rigorously the TF equation for all quadratic Hamiltonians.

Vortex configurations in the two-dimensional torus are considered in noncommu-tative space. We analyze the BPS equations of the Abelian Higgs model. Numerical solutions are constructed for the self-dual and anti-self dual cases by extending an algorithm originally developed for ordinary commutative space. We work within the Fock space approach to noncommutative theories and the Moyal-Weyl conne...

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...