We consider a Riemannian spin manifold (M, g) with a fixed spin structure. The zero sets of solutions of generalized Dirac equations on M play an important role in some questions arising in conformal spin geometry and in mathematical physics. In this setting the mass endomorphism has been defined as the constant term in an expansion of Green’s function for the Dirac operator. One is interested ...

The Dirac theory is completely reformulated in terms of Spacetime Algebra, a real Clifford Algebra characterizing the geometrical properties of spacetime. This eliminates redundancy in the conventional matrix formulation and reveals a hidden geometric structure in the theory. Among other things, it reveals that complex numbers in the Dirac equation have a kinematical interpretation, with the un...

The Dirac equation serves as the basis for the relativistic description of atoms, nuclei and hadrons. In atoms the relevant potentials felt by the electron are Coulombic vector potentials. A Dirac Hamiltonian with a Coulomb potential exhibits a finestructure spectrum with characteristic two-fold degeneracy. Relativistic mean fields in nuclei generated by meson exchanges , and quark confinement ...

We present an ARPES study of the surface states of Ru2Sn3, a new type of a strong 3D topological insulator (TI). In contrast to currently known 3D TIs, which display two-dimensional Dirac cones with linear isotropic dispersions crossing through one point in the surface Brillouin Zone (SBZ), the surface states on Ru2Sn3 are highly anisotropic, displaying an almost flat dispersion along certain h...

We introduce the magnetic angular momentum as a consequence of the structure of the sO(3) Lie algebra defined by the Feynman brackets. The Poincaré momentum and Dirac magnetic monopole appears as a direct result of this framework.

In this work, we consider the deforming of a G2 structure by a vector field on a 7−manifold. To obtain the metric corresponding to deformed G2 structure, a new map is defined. By using this new map, the covariant derivatives on associated spinor bundles are compared. Then, the relation between Dirac operators on spinor bundles are investigated under some restrictions.

We consider radiative β-decay of the neutron in heavy baryon chiral perturbation theory. Nucleon-structure effects not encoded in the weak coupling constants gA and gV are determined at next-to-leading order in the chiral expansion, and enter at the [Formula: see text]-level, making a sensitive test of the Dirac structure of the weak currents possible.

We construct some natural metric connections on metric contact manifolds compatible with the contact structure and characterized by the Dirac operators they determine. In the case of CR manifolds these are invariants of a fixed pseudo-hermitian structure, and one of them coincides with the Tanaka–Webster connection.  2005 Elsevier B.V. All rights reserved. MSC: 53B05; 53C15; 53D10; 53D15

We investigate the index of the Neuberger’s Dirac operator in abelian gauge theories on finite lattices by numerically analyzing the spectrum of the hermitian Wilson-Dirac operator for a continuous family of gauge fields connecting different topological sectors. By clarifying the characteristic structure of the spectrum leading to the index theorem we show that the index coincides to the topolo...

A brief pedagogical survey of the star product is provided, through Groenewold’s original construction based on the Weyl correspondence. It is then illustrated how simple Landau orbits in a constant magnetic field, through their Dirac Brackets, define a noncommutative structure since these brackets exponentiate to a star product—a circumstance rarely operative for generic Dirac Brackets. The ge...