Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · hep-lat/0103024

General Ginsparg-Wilson fermions and index

Werner Kerler
View original source ↗Read source document ↗Export metadata ↓

Abstract

We show rigorously that for general Ginsparg-Wilson fermions the dimensions of the geometric eigenspace and of the algebraic one for zero modes agree so that the index theorem on the lattice is not spoiled by unwanted additional terms.

Explore related subjects

hep-lat

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Werner Kerler. 2001-03-22. General Ginsparg-Wilson fermions and index. https://doi.org/10.1016/s0370-2693(01)00581-0

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Accurate Sampling from Diffusion Models

A new proposal called DM-SMC (Diffusion Model - Sequential Monte Carlo) is investigated, which samples ensembles defined in terms of an action, using diffusion models trained on samples from the ensemble. The SMC setup allows for accurate sampling in spite of an approximate diffusion model and the finite stepsize used in the numerical solution of the stochastic process. Improved update strategies are also investigated. Results are presented for a $Z_2$ symmetric scalar field theory in 2 dimensions near its 2nd order phase transition.

hep-lat↗
arXiv2026

Decomposition of the axial-vector current in a finite box

We consider the matrix element of the axial-vector current between two nucleon states in a finite box. Starting from the chiral Lagrangian density with nucleon and Delta-isobar degrees of freedom, we study the finite-volume effects at the one-loop level. We show that the standard decomposition into the axial-vector and pseudoscalar form factor is incomplete in a finite box. We derive expressions for the complete set of in-box form factors at one loop, and demonstrate how to extract the full set from lattice correlation functions. We verify that the axial Ward identity holds in the chiral limit. We derive the one-loop expressions for the pseudoscalar form factor and verify that the in-box axial Ward identity away from the chiral limit is fulfilled also. Selected numerical results are shown for two flavor-SU(2) lattice ensembles. Sizable finite-volume effects are observed, with an important role for the Delta-isobar. We discuss the implications of our results for lattice studies of the axial-vector current. We conclude that full finite-box results are crucial for a precise determination of the form factors.

hep-lat↗
arXiv2026

A variational framework for variance reduction in lattice field theory

The signal-to-noise problem limits the reach of many lattice calculations. We present a variational framework that recasts it as a transport problem: the loss of signal reflects a mismatch between the distribution one samples and the one needed to measure an observable, and can be reduced by transporting configurations to close that gap. The optimal transport is typically determined either through a stochastic estimator based on Langevin dynamics or by parametrising it as a normalising flow trained with automatic differentiation. We discuss how the framework brings these methods under a common variational principle and present results for scalar theories.

hep-lat↗