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...

Abelian deformations of ordinary algebras of functions are studied. The role of Harrison cohomology in classifying such deformations is illustrated in the context of simple examples chosen for their relevance to physics. It is well known that Harrison cohomology is trivial on smooth manifolds and that, consequently, abelian ∗-products on such manifolds are trivial to first order in the deformat...

We relate the Bohr-Sommerfeld conditions established in λ-microlocal analysis to formal deformation quantization of symplectic manifolds by classifying star products adapted to some Lagrangian sub-manifold L, i.e. products preserving the classical vanishing ideal IL of L up to IL-preserving equivalences.

We study deformation quantization on an infinite-dimensional Hilbert space W endowed with its canonical Poisson structure. The standard example of the Moyal star-product is made explicit and it is shown that it is well defined on a subalgebra of C(W ). A classification of inequivalent deformation quantizations of exponential type, containing the Moyal and normal star-products, is also given.

The Weyl-Wigner map yields the entire structure of Moyal quantum mechanics directly from the standard operator formulation. The covariant generalization of Moyal theory, also known as Vey quantum mechanics, was presented in the literature many years ago. However, a derivation of the formalism directly from standard operator quantum mechanics, clarifying the relation between the two formulations...

We study the canonical quantization of the induced 2d-gravity and the pure gravity CGHS-model on a closed spatial section. The Wheeler-DeWitt equations are solved in (spatially homogeneous) choices of the internal time variable and the space of solutions is properly truncated to provide the physical Hilbert space. We establish the quantum equivalence of both models and relate the results with t...

TheWigner phase-space distribution function provides the basis for Moyal’s deformation quantization alternative to the more conventional Hilbert space and path integral quantizations. General features of time-independent Wigner functions are explored here, including the functional (“star”) eigenvalue equations they satisfy; their projective orthogonality spectral properties; their Darboux (“sup...

Abelian deformations of ordinary algebras of functions are studied. The role of Harrison cohomology in classifying such deformations is illustrated in the context of simple examples chosen for their relevance to physics. It is well known that Harrison cohomology is trivial on smooth manifolds and that, consequently, abelian ∗-products on such manifolds are trivial to first order in the deformat...