Related papers: Chiral Anomaly for a New Class of Lattice Dirac Op…
A new class of lattice Dirac operators $D$ have been recently proposed on the basis of the generalized Ginsparg-Wilson relation, $\gamma_5(\gamma_5 D) + (\gamma_5 D)\gamma_5 =2a^{2k+1}(\gamma_5 D)^{2k+2}$, where $k$ is a non-negative…
Recent studies of the topological properties of a general class of lattice Dirac operators are reported. This is based on a specific algebraic realization of the Ginsparg-Wilson relation in the form…
The Ginsparg-Wilson relation $D \gamma_5 + \gamma_5 D = 2 a D R \gamma_5 D$ with $R = (a \gamma_5 D)^{2k}$ is discussed. An explicit realization of D is constructed. It is shown that this sequence of topologically-proper lattice Dirac…
A specific algebraic realization of the Ginsparg-Wilson relation in the form $\gamma_{5}(\gamma_{5}D)+(\gamma_{5}D)\gamma_{5} = 2a^{2k+1}(\gamma_{5}D)^{2k+2}$ is discussed, where $k$ stands for a non-negative integer and $k=0$ corresponds…
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 perturbative study of a general class of lattice Dirac operators is reported, which is based on an algebraic realization of the Ginsparg-Wilson relation in the form $\gamma_{5}(\gamma_{5}D)+(\gamma_{5}D)\gamma_{5} =…
In the continuum, a topological obstruction to the vanishing of the non-abelian anomaly in 2n dimensions is given by the index of a certain Dirac operator in 2n+2 dimensions, or equivalently, the index of a 2-parameter family of Dirac…
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…
The condition for a lattice Dirac operator D to reproduce correct chiral anomaly at each site of a finite lattice for smooth background gauge fields is that D possesses exact zero modes satisfying the Atiyah-Singer index theorem. This is…
We clarify the questions rised by a recent example of a lattice Dirac operator found by Chiu. We show that this operator belongs to a class based on the Cayley transformation and that this class on the finite lattice generally does not…
Normality of the Dirac operator is shown to be necessary for chiral properties. From the global chiral Ward identity, which in the continuum limit gives the index theorem, a sum rule results which constrains the spectrum. The…
The axial anomaly of Ginsparg-Wilson fermion operator $D$ is discussed in general for the operator $R$ which enters the chiral symmetry breaking part in the Ginsparg-Wilson relation. The axial anomaly and the index of $D$ as well as the…
We show that, with an appropriate choice of a Dirac operator, there is a remnant of chiral anomalies in the reduced model in which there is no coordinate dependences of the gauge field. This result is obtained by exploring a topological…
A recent proposal suggests that even if a Ginsparg-Wilson lattice Dirac operator does not possess any topological zero modes in topologically-nontrivial gauge backgrounds, it can reproduce correct axial anomaly for sufficiently smooth gauge…
The relation $Tr \gamma_{5}= 0$ implies the contribution to the trace from unphysical (would-be) species doublers in lattice gauge theory. This statement is also true for the Pauli-Villars regularization in continuum theory. If one insists…
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…
Normality in connection with $\gamma_5$-hermiticity determines the basic chiral properties and rules. The Ginsparg-Wilson (GW) relation is one of the allowed constraints on the spectrum. Interrelations between features of the spectrum, the…
It is shown that the local axial anomaly in $2-$dimensions emerges naturally if one postulates an underlying noncommutative fuzzy structure of spacetime . In particular the Dirac-Ginsparg-Wilson relation on ${\bf S}^2_F$ is shown to contain…
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…
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…