相关论文: The overlap Dirac operator as a continued fraction
Evaluation of the continuum limit of the axial anomaly and index is sketched for the staggered overlap Dirac operator. There are new complications compared to the usual overlap case due to the distribution of the spin and flavor components…
As shown in earlier work, skew-adjoint linear differential operators, mapping efforts into flows, give rise to Dirac structures on a bounded spatial domain by a proper definition of boundary variables. In the present paper this is extended…
The properties of the spectrum of the overlap Dirac operator and their relation to random matrix theory are studied. In particular, the predictions from chiral random matrix theory in topologically non-trivial gauge field sectors are…
We investigate the eigenvalues of nearly chiral lattice Dirac operators constructed with five-dimensional implementations. Allowing small violation of the Ginsparg-Wilson relation, the HMC simulation is made much faster while the…
We consider supersymmetric quantum mechanical systems in arbitrary dimensions on curved spaces with nontrivial gauge fields. The square of the Dirac operator serves as Hamiltonian. We derive a relation between the number of supercharges…
Critical slowing down for the Krylov Dirac solver presents a major obstacle to further advances in lattice field theory as it approaches the continuum solution. We propose a new multi-grid approach for chiral fermions, applicable to both…
A new class of lattice Dirac operators which satisfy the index theorem have been recently proposed on the basis of the algebraic relation $\gamma_{5}(\gamma_{5}D) + (\gamma_{5}D)\gamma_{5} = 2a^{2k+1}(\gamma_{5}D)^{2k+2}$. Here $k$ stands…
In a system where chiral symmetry is spontaneously broken, the low energy eigenmodes of the continuum Dirac operator are extended. On the lattice, due to discretization effects, the Dirac operator can have localized eigenmodes that affect…
It is shown that the eigenvalue problem for the hermitian Wilson-Dirac operator of for a uniform magnetic field in two dimensions can be reduced to one-dimensional problem described by a relativistic analog of the Harper equation. An…
We expand the most general lattice Dirac operator D in a basis of simple operators. The Ginsparg-Wilson equation turns into a system of coupled quadratic equations for the expansion coefficients. Our expansion of D allows for a natural…
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 present an acceleration of the well-established Krylov-Ritz methods to compute the sign function of large complex matrices, as needed in lattice QCD simulations involving the overlap Dirac operator at both zero and nonzero baryon…
We compute the ratio $\Lambda_L/\Lambda_{\bar{MS}}$ between the scale parameter $\Lambda_L$, associated with a lattice formulation of QCD using the overlap-Dirac operator, and $\Lambda_{\bar{MS}}$ of the $\bar{\rm MS}$ renormalization…
We analyze the limit of the spectrum of a geometric Dirac-type operator under a collapse with bounded diameter and bounded sectional curvature. In the case of a smooth limit space B, we show that the limit of the spectrum is given by the…
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…
We discuss the steps to construct Dirac operators which have arbitrary fermion offsets, gauge paths, a general structure in Dirac space and satisfy the basic symmetries (gauge symmetry, hermiticity condition, charge conjugation, hypercubic…
According to the necessary requirements for a chirally symmetric Dirac operator, we present a systematic construction of such operators. We formulate a criterion for the hermitian operator which enters the construction such that the doubled…
The overlap formula for the chiral determinant is presented and the realization of gauge anomalies and gauge field toplogy in this context is discussed. The ability of the overlap formalism to deal with supersymmetric theories and…
We present a matrix technique to obtain the spectrum and the analytical index of some elliptic operators defined on compact Riemannian manifolds. The method uses matrix representations of the derivative which yield exact values for the…
We briefly review the overlap formalism for chiral gauge theories, the overlap Dirac operator for massless fermions and its connection to domain wall fermions. We describe properties of the overlap Dirac operator, and methods to implement…