We re-examine the question of quantum oscillations from surface Fermi arcs and chiral modes in Weyl semimetals. By introducing two tools--semiclassical phase-space quantization and a numerical implementation of a layered construction of Weyl semimetals--we discover several important generalizations to previous conclusions that were implicitly tailored to the special case of identical Fermi arcs...

Solutions to the four-dimensional Euclidean Weyl equation in the background of a general JNR N -instanton are known to be normalisable and regular throughout four-space. We show that these solutions are asymptotically given by a linear combination of simple singular solutions to the free Weyl equation, which can be interpreted as localised spinors. The ‘spinorial’ data parameterising the asympt...

We consider a classical Hamiltonian H on R, invariant by a Lie group of symmetry G, whose Weyl quantization Ĥ is a selfadjoint operator on L(R). If χ is an irreducible character of G, we investigate the spectrum of its restriction Ĥχ to the symmetry subspace L2χ(R ) of L(R) coming from the decomposition of Peter-Weyl. We give semi-classical Weyl asymptotics for the eigenvalues counting function...

The Misra-Miwa v-deformed Fock space is a representation of the quantized affine algebra Uv(ŝl`). It has a standard basis indexed by partitions and the non-zero matrix entries of the action of the Chevalley generators with respect to this basis are powers of v. Partitions also index the polynomial Weyl modules for Uq(glN ) as N tends to infinity. We explain how the powers of v which appear in t...

A theoretical foundation for a generalization of the elliptic difference Painlevé equation to higher dimensions is provided in the framework of birational Weyl group action on the space of point configurations in general position in a projective space. By introducing an elliptic parametrization of point configurations, a realization of the Weyl group is proposed as a group of Cremona transforma...