Optimised Dirac Operators on the Lattice: Construction, Properties and Applications

Abstract

We review a number of topics related to block variable renormalisation group transformations of quantum fields on the lattice, and to the emerging perfect lattice actions. We first illustrate this procedure by considering scalar fields. Then we proceed to lattice fermions, where we discuss perfect actions for free fields, for the Gross-Neveu model and for a supersymmetric spin model. We also consider the extension to perfect lattice perturbation theory, in particular regarding the axial anomaly and the quark gluon vertex function. Next we deal with properties and applications of truncated perfect fermions, and their chiral correction by means of the overlap formula. This yields a formulation of lattice fermions, which combines exact chiral symmetry with an optimisation of further essential properties. We summarise simulation results for these so-called overlap-hypercube fermions in the two-flavour Schwinger model and in quenched QCD. In the latter framework we establish a link to Chiral Perturbation Theory, both, in the p-regime and in the epsilon-regime. In particular we present an evaluation of the leading Low Energy Constants of the chiral Lagrangian - the chiral condensate and the pion decay constant - from QCD simulations with extremely light quarks.

published version (plus slight extension), 120 pages, 41 figures

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Cited by in corpus (7)

• Light Hadron Masses from Lattice QCD
• Precision study of the SU(3) topological susceptibility in the continuum
• Cosmic Rays and the Search for a Lorentz Invariance Violation
• Numerical properties of staggered quarks with a taste-dependent mass term
• A Numerical Study of the 2-Flavour Schwinger Model with Dynamical Overlap Hypercube Fermions
• Nucleon form factors on the lattice with light dynamical fermions
• Lattice fermion formulation via Physics-Informed Neural Networks: Ginsparg-Wilson relation and Overlap fermions