Related papers: Tricks to implement the overlap Dirac operator

The Moutard transformation for a two-dimensional Dirac operator with a complex-valued potential is constructed. It is showed that this transformation relates the potentials of Weierstrass representations of surfaces related by a composition…

We give several algorithms addressing computations of intersections of conjugate subgroups.

We study sub-Dirac operators that are associated with left-invariant bracket-generating sub-Riemannian structures on compact quotients of nilpotent semi-direct products $G=\mathbb{R}^n\rtimes_A\mathbb{R}$. We will prove that these operators…

The processing of signals on simplicial and cellular complexes defined by nodes, edges, and higher-order cells has recently emerged as a principled extension of graph signal processing for signals supported on more general topological…

This note discusses how an operator analog of the Lagrange polynomial naturally arises in the quantum-mechanical problem of constructing an explicit form of the spin projection operator.

The nature of so-called differential-algebraic operators and their approximations is constitutive for the direct treatment of higher-index differential-algebraic equations. We treat first-order differential-algebraic operators in detail and…

We show how to introduce a quark chemical potential in the overlap Dirac operator. The resulting operator satisfies a Ginsparg-Wilson relation and has exact zero modes. It is no longer gamma_5-hermitian, but its nonreal eigenvalues still…

We prove that canonical Dirac expression with linear potential generates operators on axis and half axis, for which we can find the eigenvalues and eigenfunctions in explicit form. We construct the perturbations of these operators with in…

We present some results of a numerical investigation of the 't Hooft model with 2,3 and 4 colors, regularized on the lattice with overlap fermions.

We find and classify possible equivariant spin structures with Dirac operators on the noncommutative torus, proving that similarly as in the classical case the spectrum of the Dirac operator depends on the spin structure.

We give a local formula for the index of a transverse Dirac-type operator on a compact manifold with a Riemannian foliation, under the assumption that the Molino sheaf is a sheaf of abelian Lie algebras.

The purpose of this survey is to summarize known results about tropical hypersurfaces and the Cayley Trick from polyhedral geometry. This allows for a systematic study of arrangements of tropical hypersurfaces and, in particular,…

We present methods for obtaining new solutions to the bispectral problem. We achieve this by giving its abstract algebraic version suitable for generalizations. All methods are illustrated by new classes of bispectral operators.

We study the two-dimensional Dirac operator with an arbitrary combination of electrostatic and Lorentz scalar $\delta$-interactions of constant strengths supported on a smooth closed curve. For any combination of the coupling constants a…

We compute the Dirac spectrum of SU(3) for a one parameter family of Dirac operators, including the Levi-Civita, cubic, and trivial Dirac operators. We then proceed to compute the spectral action for the entire family.

The necessary and sufficient conditions are given for a sequence of complex numbers to be the periodic (or antiperiodic) spectrum of non-self-adjoint Dirac operator.

In this proceeding we propose a new procedure to impose the Schroedinger functional Dirichlet boundary condition on the overlap Dirac operator and the domain-wall fermion using an orbifolding projection. With this procedure the zero mode…

We give an index formula for a class of Dirac operators coupled with unbounded potentials. More precisely, we study operators of the form P := D+ V, where D is a Dirac operators and V is an unbounded potential at infinity on a possibly…

In this note, we explain how the f-invariant of a circle transfer can be computed on the framed manifold itself in terms of the spectral asymmetry of twisted Dirac operators on the base. Some explicit examples and a treatment of the…

Three aspects of symmetry structure of lattice chiral fermion in the overlap formalism are discussed. By the weak coupling expansion of the overlap Dirac operator, the axial anomaly associated to the chiral transformation proposed by…