In various dimensional euclidean lattice gauge theories, we examine a compatibility of the Majorana decomposition and the charge conjugation property of lattice Dirac operators. In 8n and 1+8n dimensions, we find a difficulty to decompose a classical lattice action of the Dirac fermion into a system of the Majorana fermion and thus to obtain a factrized form of the Dirac determinant. Similarly,...

Recently, it has been pointed out that dimensionless actions in four dimensional curved spacetime possess a symmetry which goes beyond scale invariance but is smaller than full Weyl invariance. This symmetry was dubbed restricted Weyl invariance. We show that starting with a restricted Weyl invariant action that includes a Higgs sector with no explicit mass, one can generate the Einstein-Hilber...

Following a purely algebraic procedure, we provide an exhaustive classification of local Weyl-invariant scalar densities in dimension D = 8 .

The model of the bosonic string with the noncommutative world-sheet geometry is proposed in the framework of Fedosov's deformation quantization. The re-interpretation of the model in terms of bosonic string coupled to infinite multiplet of background fields is given and the link to the W-symmetry is discussed. For the case of d=4 Euclidean target space, the stringy counterparts of the Yang-Mill...

...

Though the Weyl tensor is a linear combination of the curvature tensor, Ricci tensor and Ricci scalar, it does not have all and only the Lie symmetries of these tensors since it is possible, in principle, that “asymmetries cancel”. Here we investigate if, when and how the symmetries can be different. It is found that we can obtain a metric with a finite dimensional Lie algebra of Weyl symmetrie...

A system of PDOs(=Partial Differential Operators) has two non-commutativities, (i) one from [∂q, q] = 1 (Heisenberg relation), (ii) the other from [A, B] 6= 0 for A, B being matrices in general. Non-commutativity from Heisenberg relation is nicely controlled by using Fourier transformations (i.e. the theory of ΨDOs=pseudo-differential operators). Here, we give a new method of treating non-commu...

The theme of this work is that the theory of charged particles in a uniform magnetic field can be generalized to a large class of operators if one uses an extended a class of Weyl operators which we call ”Landau–Weyl pseudodifferential operators”. The link between standard Weyl calculus and Landau–Weyl calculus is made explicit by the use of an infinite family of intertwining ”windowed wavepack...

NbP is a recently realized Weyl semimetal (WSM), hosting Weyl points through which conduction and valence bands cross linearly in the bulk and exotic Fermi arcs appear. The most intriguing transport phenomenon of a WSM is the chiral anomaly-induced negative magnetoresistance (NMR) in parallel electric and magnetic fields. In intrinsic NbP the Weyl points lie far from the Fermi energy, making ch...

Weyl semimetals are paradigmatic topological gapless phases in three dimensions. We here address the effect of disorder on charge transport in Weyl semimetals. For a single Weyl node with energy at the degeneracy point and without interactions, theory predicts the existence of a critical disorder strength beyond which the density of states takes on a nonzero value. Predictions for the conductiv...