We prove that the massless Dirac operator in R with long-range potential has an a.c. spectrum which fills the whole real line. The Dirac operators with matrix-valued potentials are considered as well.

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...

We show how the standard domain wall action can be simply modified to allow arbitrarily exact chiral symmetry at finite fifth dimensional extent. We note that the method can be used for both quenched and dynamical calculations. We test the method using smooth and thermalized gauge field configurations. We also make comparisons of the performance (cost) of the domain wall operator for spectrosco...

We study the behavior of the spectrum of the Dirac operator on collapsing S1-bundles. Convergent eigenvalues will exist if and only if the spin structure is projectable.

Manifolds with fibered hyperbolic cusp metrics include hyperbolic manifolds with cusps and locally symmetric spaces of Q-rank one. We extend Vaillant’s treatment of Dirac-type operators associated to these metrics by weaking the hypotheses on the boundary families through the use of Fredholm perturbations as in the family index theorem of Melrose and Piazza and by treating the index of families...

We show how the standard domain wall action can be simply modified to allow arbitrarily exact chiral symmetry at finite fifth dimensional extent Ls. We note that the method can be used for both quenched and dynamical calculations. We test the method using smooth and thermalized gauge field configurations. We also make comparisons of the performance (cost) of the domain wall operator for spectro...