相关论文: Tricks to implement the overlap Dirac operator

The overlap operator is just the simplest of a class of Dirac operators with an exact chiral symmetry. I demonstrate how a general class of chiral Dirac operators can be constructed, show that they have no fermion doublers and that they are…

In this note, we give a geometric expression for the multiplicities of the equivariant index of a Dirac operator twisted by a line bundle.

In this paper, for foliations with spin leaves, we compute the spectral action for sub-Dirac operators.

The overlap Dirac operator obeys the Ginsparg-Wilson equation and offers a possibility to introduce chiral symmetry on the lattice. Evaluating the overlap operator is numerically very expensive and one has to rely on approximation methods.…

We present relaxation and preconditioning techniques which accelerate the inversion of the overlap operator by a factor of four on small lattices, with larger gains as the lattice size increases. These improvements can be used in both…

We revisit quenched reduction with fermions and explain how some old problems can be avoided using the overlap Dirac operator.

In this paper, we give a geometric expression for the multiplicities of the equivariant index of a spin-c Dirac operator.

We determine what should correspond to the Dirac operator on certain quantized hermitian symmetric spaces and what its properties are. A new insight into the quantized wave operator is obtained.

We summarize our recent investigations of lattice QCD with dynamical overlap fermions. We sketch algorithmic issues and our approach to solving them. We show our measurement of the topological susceptibility. We describe a computation of…

The overlap Dirac operator at nonzero quark chemical potential involves the computation of the sign function of a non-Hermitian matrix. In this talk we present iterative Krylov subspace approximations, with deflation of critical…

The Overlap-Dirac operator provides a lattice regularization of massless vector gauge theories with an exact chiral symmetry. Practical implementations of this operator and recent results in quenched QCD using this Overlap-Dirac operator…

We compute Neuberger's overlap operator by the Lanczos algorithm applied to the Wilson-Dirac operator. Locality of the operator for quenched QCD data and its eigenvalue spectrum in an instanton background are studied.

The overlap operator is a lattice discretization of the Dirac operator of quantum chromodynamics, the fundamental physical theory of the strong interaction between the quarks. As opposed to other discretizations it preserves the important…

I present a few new and recent ideas of the multiloop calculations.

An overview of the current status of algorithmic approaches to dynamical overlap fermions is given. In particular the issue of changing the topological sector is discussed.

The technique of differential intertwining operators (or Darboux transformation operators) is systematically applied to the one-dimensional Dirac equation. The following aspects are investigated: factorization of a polynomial of Dirac…

Improvements of various methods to compute the sign function of the hermitian Wilson-Dirac matrix within the overlap operator are presented. An optimal partial fraction expansion (PFE) based on a theorem of Zolotarev is given. Benchmarks…

The overlap hypercube fermion is constructed by inserting a lattice fermion with hypercubic couplings into the overlap formula. One obtains an exact Ginsparg-Wilson fermion, which is more complicated than the standard overlap fermion, but…

We compare the efficiency of four different algorithms to compute the overlap Dirac operator, both for the speed, i.e., time required to reach a desired numerical accuracy, and for the adaptability, i.e., the scaling of speed with the…

We review a procedure of factorizing the Minkowski space Dirac operator over a~suitable superspace, discuss its Euclidean space version and apply the worked out formalism in the case od an almost-commutative Dirac operator. The presented…