相关论文: On the definition of the covariant lattice Dirac o…
The gauge covariant lattice Dirac operator D which has recently been proposed by Neuberger satisfies the Ginsparg-Wilson relation and thus preserves chiral symmetry. The operator also avoids a doubling of fermion species, but its locality…
We present a detailed study of the interplay between chiral symmetry and spectral properties of the Dirac operator in lattice gauge theories. We consider, in the framework of the Schwinger model, the fixed point action and a fermion action…
We construct a lattice Dirac operator of overlap type that describes the propagation of a Dirac fermion in an external gravitational field. The local Lorentz symmetry is manifestly realized as a lattice gauge symmetry, while it is believed…
A new class of lattice Dirac operators $D$ 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 $k$…
A remarkable feature of a lattice Dirac operator is discussed. Unlike the Dirac operator for massless fermions in the continuum, this Ginsparg-Wilson lattice Dirac operator does not possess topological zero modes for any…
We study the implications of the index theorem and chiral Jacobian in lattice gauge theory, which have been formulated by Hasenfratz, Laliena and Niedermayer and by L\"{u}scher, on the continuum formulation of the chiral Jacobian and…
L\"uscher's recent formulation of Abelian chiral gauge theories on the lattice, in the vacuum (or perturbative) sector in infinite volume, is reinterpreted in terms of the lattice covariant regularization. The gauge invariance of the…
Using the tools of noncommutative geometry we calculate the distances between the points of a lattice on which the usual discretized Dirac operator has been defined. We find that these distances do not have the expected behaviour, revealing…
We mathematically show an equality between the index of a Dirac operator on a flat continuum torus and the $\eta$ invariant of a lattice Dirac operator known as the Wilson Dirac operator with a negative mass when the lattice spacing is…
We discuss a proposal for the construction of lattice QCD with gauge action, fermionic action, theta-term, and the operators all based on the lattice Dirac operator D with exact chiral symmetry. The simplest regularization of this type uses…
A novel feature of a Ginsparg-Wilson lattice Dirac operator is discussed. Unlike the Dirac operator for massless fermions in the continuum, this lattice Dirac operator does not possess topological zero modes for any topologically-nontrivial…
We show that even if a lattice Dirac operator satisfies the conditions consisting of locality, free of species doublings, correct continuum behavior, $\gm5$-hermiticity and the Ginsparg-Wilson relation, it does not necessarily have exact…
A lattice action for QED is considered, where the derivatives in the Dirac operator are replaced by one-sided lattice differences. A systematic expansion in the lattice spacing of the one-loop contribution to the fermion self energy, vacuum…
The fermionic topological charge of lattice gauge fields, given in terms of a spectral flow of the Hermitian Wilson--Dirac operator, or equivalently, as the index of Neuberger's lattice Dirac operator, is shown to have analogous properties…
We revisit the lattice index theorem in the perspective of $K$-theory. The standard definition given by the overlap Dirac operator equals to the $\eta$ invariant of the Wilson Dirac operator with a negative mass. This equality is not…
It was recently proposed by the second author to consider lattice formulations of QCD in which complete actions, including the gauge part, are built explicitly from a given Dirac operator D. In a simple example of such theory, the gauge…
It is shown that the nonlocal Dirac operator yielded by a lattice model that preserves chiral symmetry and uniqueness of fields, approaches to an ultralocal and invariant under translations operator when the size of the lattice tends to…
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,…
We discuss how to formulate Dirac fermion operator on a finite lattice such that it can provide a nonperturbative regularization for massless fermion interacting with a background gauge field.
The chiral Jacobian, which is defined with Neuberger's overlap Dirac operator of the lattice fermion, is explicitly evaluated in the continuum limit without expanding it in the gauge coupling constant. Our calculational scheme is simple and…