A massless electroweak theory for leptons is formulated in a Weyl space, W4, yielding a Weyl invariant dynamics of a scalar field φ, chiral Dirac fermion fields ψL and ψR, and the gauge fields κμ, Aμ, Zμ,Wμ and W † μ allowing for conformal rescalings of the metric gμν and all fields with nonvanishing Weyl weight together with the corresponding transformations of the Weyl vector fields, κμ, repr...

In this paper it is shown that a Lanczos potential for the Weyl curvature tensor does not exist for all spaces of dimension n ≥ 7. Whether there exists a Lanczos potential [1] for Weyl curvature tensors in dimensions n > 4 has still not been determined. Although Lanczos's original proof [1] for existence was flawed [2], there have subsequently been complete proofs for existence in four dimensio...

On a (pseudo-) Riemannian manifold of dimension n > 3, the space of tensors which transform covariantly under Weyl rescalings of the metric is built. This construction is related to a Weyl-covariant operator D whose commutator [D,D] gives the conformally invariant Weyl tensor plus the Cotton tensor. So-called generalized connections and their transformation laws under diffeomorphisms and Weyl r...

We propose to realize Weyl semimetals in a cubic optical lattice. We find that there exist three distinct Weyl semimetal phases in the cubic optical lattice for different parameter ranges. One of them has two pairs of Weyl points and the other two have one pair of Weyl points in the Brillouin zone. For a slab geometry with (010) surfaces, the Fermi arcs connecting the projections of Weyl points...

The notion of a Weyl module, previously defined for the untwisted affine algebras, is extended here to the twisted affine algebras. We describe an identification of the Weyl modules for the twisted affine algebras with suitably chosen Weyl modules for the untwisted affine algebras. This identification allows us to use known results in the untwisted case to compute the dimensions and characters ...

In this paper we develop a relative Gröbner basis method for a wide class of filtered modules. Our general setting covers the cases of modules over rings of differential, difference, inversive difference and difference– differential operators, Weyl algebras and multiparameter twisted Weyl algebras (the last class of rings includes the classes of quantized Weyl algebras and twisted generalized W...

Weyl fermions are massless chiral particles first predicted in 1929 and once thought to describe neutrinos. Although never observed as elementary particles, quasiparticles with Weyl dispersion have recently been experimentally discovered in solid-state systems causing a furore in the research community. Systems with Weyl excitations can display a plethora of fascinating phenomena and offer grea...

863 news & views and patterning, opens up a wide range of new applications for hot-electron-driven chemistry. The LEE source might also prove a critical tool for obtaining a deeper nanoscale understanding of radiation chemistry and biology, and material degradation by high-energy radiation in general. The quantum description of spin-1/2 particles is given by the solutions of the Dirac equation....