Related papers: A confederacy of anomalies
I explore the non-perturbative issues entwining lattice gauge theory, anomalies, and chiral symmetry. After briefly reviewing the importance of chiral symmetry in particle physics, I discuss how anomalies complicate lattice formulations.…
I review the ongoing attempts to define chiral gauge theories using the lattice regularization.
A few subjects which strongly intertwine our field are discussed: K --> Pi Pi decay, chiral symmetry on the lattice and a few other selected topics. Open questions are touched also on perturbation theory, locality, Gribov copies, CP…
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…
This write-up starts by introducing lattice chirality to people possessing a fairly modern mathematical background, but little prior knowledge about modern physics. I then proceed to present two new and speculative ideas.
The Wilson formulation of fermions in lattice gauge theory provides a unified description of the chiral anomalies in the standard model. The discrete Dirac operator diagonalizes into a series of two by two blocks. In each block the possible…
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.
A recent proposal by Kaplan for a chiral gauge theory on the lattice is tested with background gauge fields. The spectrum of the finite lattice Hamiltonian is calculated and the existence of a chiral fermion is demonstrated. Lattice…
Some key features of continuum chiral fermions are shown to be satisfied by the overlap.
Dirac fermions coupled to gauge fields can exhibit the chiral anomaly even on a finite spatial lattice. A careful description of this phenomenon yields new insights into the nature of spin-charge relations and on-site symmetries (symmetries…
Within the overlap framework, I derive the main formulae one finds today in papers touting a ``new approach'' to the regularization of chiral gauge theories. My main objective is to clear up an unhealthy confusion about how many successful…
We present a method for implementing gauge theories of chiral fermions on the lattice.
A global anomaly in a chiral gauge theory manifests itself in different ways in the continuum and on the lattice. In the continuum case, functional integration of the fermion determinant over the whole space of gauge fields yields zero. In…
Lattice gauge theory and chiral perturbation theory are among the primary tools for understanding non-perturbative aspects of QCD. I review several subtle and sometimes controversial issues that arise when combining these techniques. Among…
A popular approximation in lattice gauge theory is an extrapolation in the number of fermion species away from the four fold degeneracy natural with the staggered fermion formulation. I show that the extrapolation procedure mutilates the…
Summary talk presented at the Conference on Lattice Field Theory, Amsterdam, September, 1992. Abstract: The status of several proposals for defining a theory of chiral fermions on the lattice is reviewed and some new estimates for the upper…
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
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…
We investigate a proposal for the construction of models with chiral fermions on the lattice using staggered fermions. In this approach the gauge invariance is broken by the coupling of the staggered fermions to the gauge fields. We aim at…
Contents: 1. Introduction, 2. Chiral gauge theories & the gauge anomaly, 3. The regularization problem, 4. Weyl fermions from 4+1 dimensions, 5. The Ginsparg-Wilson relation, 6. Gauge-invariant lattice regularization of anomaly-free…