We predict a family of 2D carbon (C) allotropes, square graphynes (S-graphynes) that exhibit highly anisotropic Dirac fermions, using first-principle calculations within density functional theory. They have a square unit-cell containing two sizes of square C rings. The equal-energy contour of their 3D band structure shows a crescent shape, and the Dirac crescent has varying Fermi velocities fro...

In the model of topological particles we have four types topologically stable dual Dirac monopoles with soft core and finite mass. We discuss steps how to get a equation for these particles. show free interacting case that arrive at in limit, where solitons approach singular monopoles.

The name Dirac oscillator was first introduced by Moshinky and Szczepaniak [1] for a Dirac equation in which the momentum p is replaced by p → p−imωβr with r being the position vector, m the mass of the particle and ω the frequency of the oscillator. The name was given because the determination of the spectrum and eigenstate of a Dirac oscillator [1] was obtained from that of an ordinary oscill...

We describe the Dirac monopole using the Cheeger-Simons differential characters. We comment on the rôle of the Dirac string and on the connection with Deligne cohomology.

In this paper we define tau functions for holonomic fields associated with the Dirac operator on the Poincare disk. The deformation analysis of the tau functions is worked out and in the case of the two point function, the tau function is expressed in terms of a Painleve function of type VI.

Heat kernels are used in this paper to express the analytic index of projectively invariant Dirac type operators on Γ covering spaces of compact manifolds, as elements in the K-theory of certain unconditional completions of the twisted group algebra of Γ. This is combined with V. Lafforgue’s results in the untwisted case, to compute the range of the trace on the K-theory of these algebras, unde...

As a tool to carry out the quantization of gauge theory on a noncommutative space, we present a Dirac operator that behaves as a line element of the canonical noncommutative space. Utilizing this operator, we construct the Dixmier trace, which is the regularized trace for infinite-dimensional matrices. We propose the possibility of solving the cosmological constant problem by applying our gauge...