相关论文: Analytic progress on exact lattice chiral symmetry
During the last several years a non-perturbative formulation of exact chiral symmetry on the lattice has been developed. I shall outline the main ideas of these developments and discuss prospects for the future. The focus will be on the…
It has been shown recently that Dirac operators satisfying the Ginsparg-Wilson relation provide a solution of the chirality problem in QCD at finite lattice spacing. We discuss different ways to construct these operators and their…
It is shown that the Ginsparg-Wilson relation implies an exact symmetry of the fermion action, which may be regarded as a lattice form of an infinitesimal chiral rotation. Using this result it is straightforward to construct lattice Yukawa…
I review the substantial progress which has been made recently with the non-perturbative construction of chiral gauge theories on the lattice. In particular, I discuss three different approaches: a gauge invariant method using fermions…
As a non-perturbative and gauge invariant regularization the lattice provides a tool for deeper understanding of the celebrated Yang-Mills theory, QCD and chiral gauge theories. For illustration, I discuss some analytic developments on the…
A recently proposed formulation of chiral lattice gauge theories is reviewed, in which the locality and gauge invariance of the theory can be preserved if the fermion representation of the gauge group is anomaly-free.
We derive Ginsparg-Wilson relation for a lattice chiral symmetry in theories with self-interacting fermions. Auxiliary scalar and pseudo-scalar fields are introduced on a coarse lattice to give an effective description of the fermionic…
We discuss how to construct anomaly-free chiral gauge theories on the lattice with exact gauge invariance in the framework of domain wall fermion. Chiral gauge coupling is realized by introducing a five-dimensional gauge field which…
The Ginsparg-Wilson(G-W) relation for chiral symmetry is extended for a supersymmetrical(SUSY) case on a lattice. It is possible to define exact lattice supersymmetry which are devided into two different cases according to using difference…
This is a review of the status and outstanding issues in attempts to construct chiral lattice gauge theories by decoupling the mirror fermions from a vectorlike theory. In the first half, we explain why studying nonperturbative chiral gauge…
I discuss some of the difficulties with formulating chiral symmetry on the lattice and review a recently proposed scheme for a fully finite and exactly gauge invariant lattice regularization of the standard model.
A brief summary of lattice fermions defined by the general Ginsparg-Wilson algebra is first given. It is then shown that those general class of fermion operators have a conflict with CP invariance in chiral gauge theory and with the…
It is shown that U(1) chiral gauge theories with anomaly-free multiplets of Weyl fermions can be put on the lattice without breaking the gauge invariance or violating any other fundamental principle. The Ginsparg-Wilson relation plays a key…
The Ginsparg-Wilson (GW) relation elegantly captures how the anomalous chiral symmetry of a Dirac fermion manifests on the lattice. In this talk, we discuss how the GW relation and its closed-form solution, the overlap operator, can be…
The $SU(N_f)_L \otimes SU(N_f)_R$ chiral symmetry of QCD is of central importance for the nonperturbative low-energy dynamics of light quarks and gluons. Lattice field theory provides a theoretical framework in which these dynamics can be…
The status of lattice calculations in Quantum Field Theory is reviewed. A major part is devoted to recent progress in formulating exact chiral symmetry on the lattice. Another topic which has received a lot of attention is the influence of…
We propose a construction of a 2-dimensional lattice chiral gauge theory. The construction may be viewed as a particular limit of an infinite warped 3-dimensional theory. We also present a "single-site'' construction using Ginsparg-Wilson…
There is a long standing challenge in lattice QCD concerning the relationship between $\mathcal{CP}$-symmetry and lattice chiral symmetry: na\"ively the chiral symmetry transformations are not invariant under $\mathcal{CP}$. With results…
The subject of these summer school lectures are (i) Chiral symmetry; (ii) Anomalies; (iii) Domain wall fermions; (iv) Overlap fermions and the Ginsparg-Wilson equation
Based upon the lattice Dirac operator satisfying the Ginsparg-Wilson relation, we investigate canonical formulation of massless fermion on the spatial lattice. For free fermion system exact chiral symmetry can be implemented without species…