A Superspace Dirac Operator in NCG and the “Factorization” of the Ordinary Dirac Operator

Dirac Cohomology for the Cubic Dirac Operator

Let g be a complex semisimple Lie algebra and let r ⊂ g be any reductive Lie subalgebra such that B|r is nonsingular where B is the Killing form of g. Let Z(r) and Z(g) be, respectively, the centers of the enveloping algebras of r and g. Using a Harish-Chandra isomorphism one has a homomorphism η : Z(g) → Z(r) which, by a well-known result of H. Cartan, yields the the relative Lie algebra cohom...

The Microscopic Dirac Operator Spectrum

We review the exact results for microscopic Dirac operator spectra based on either Random Matrix Theory, or, equivalently, chiral Lagrangians. Implications for lattice calculations are discussed.

A-Harmonic Equations and the Dirac Operator

Inverse Problem for Interior Spectral Data of the Dirac Operator with Discontinuous Conditions

In this paper, we study the inverse problem for Dirac differential operators with  discontinuity conditions in a compact interval. It is shown that the potential functions can be uniquely determined by the value of the potential on some interval and parts of two sets of eigenvalues. Also, it is shown that the potential function can be uniquely determined by a part of a set of values of eigenfun...

The Dirac operator of a graph

We discuss some linear algebra related to the Dirac matrix D of a finite simple graph G = (V,E).