Exactly massless fermions on the Lattice
نویسنده
چکیده
My talk at Lattice 98 essentially consisted of two parts : (1) The general solution of the Ginsparg-Wilson (GW) relation; (2) Some numerical results for the ( generalized ) NeubergerDirac fermion operator. In this writeup, due to the page limit, I confine my discussions to the second part of which I did not have enough time to cover in my talk. For the first part, I refer to ref. [5] and ref. [6] for details. Although the numerical results are obtained for the ( generalized ) Neuberger-Dirac fermion operator which is so far the only explicit and physical solution of the GW relation, nevertheless, they can serve the purpose to illustrate the general properties of the GW fermion. The salient feature of the GW fermion D
منابع مشابه
Topological Charge and the Spectrum of Exactly Massless Fermions on the Lattice
The square root of the positive definite hermitian operator D† wDw in Neuberger’s proposal of exactly massless quarks on the lattice is implemented by the recursion formula Yk+1 = 1 2(Yk +D † wDwY −1 k ) with Y0 = 1I, where Y 2 k converges to D † wDw quadratically. The spectrum of the lattice Dirac operator for single massless fermion in two dimensional background U(1) gauge fields is investiga...
متن کاملThe Spectrum and Topological Charge of Exactly Massless Fermions on the Lattice
The square root of the positive definite hermitian operator D† wDw in Neuberger’s proposal of exactly massless quarks on the lattice is implemented by the recursion formula Yk+1 = 1 2 (Yk +D † wDwY −1 k ) with Y0 = 1I, where Y 2 k converges to D † wDw quadratically. The spectrum of the lattice Dirac operator for single massless fermion in two dimensional background U(1) gauge fields is investig...
متن کاملParity invariant lattice regularization of three - dimensional gauge - fermion system
In three dimensions, the effective action for the gauge field induced by integrating out a massless Dirac fermion is known to give either a parity-invariant or a parity-violating result, depending on the regularization scheme. We construct a lattice formulation of the massless Dirac fermion using the overlap formalism. We show that the result is parity invariant in contrast to the formulation u...
متن کاملRU-97-84 Vector like gauge theories with almost massless fermions on the lattice.
Vector like gauge theories with almost massless fermions on the lattice. Abstract A truncation of the overlap (domain wall fermions) is studied and a criterion for reliability of the approximation is obtained by comparison to the exact overlap formula describing massless quarks. We also present a truncated version of regularized, pure gauge, supersymmetric models. The mechanism for generating a...
متن کاملRenormalization of lattice gauge theories with massless Ginsparg Wilson fermions
Using functional techniques, we prove, to all orders of perturbation theory, that lattice vector gauge theories with Ginsparg Wilson fermions are renormalizable. For two or more massless fermions, they satisfy a flavour mixing axial vector Ward identity. It involves a lattice specific part that is quadratic in the vertex functional and classically irrelevant. We show that it stays irrelevant un...
متن کاملBlock renormalization group transformations and overlap fermions
In this preliminary work, I provide the outline of an argument (leaving the full proof to a future publication) that there exists a valid renormalization group blocking transformation which converts the continuum fermion action into a Ginsparg-Wilson lattice action. I construct the blocking for the massless overlap operator as a specific example, indicating how other Ginsparg-Wilson lattice Dir...
متن کامل