The Schrödinger functional in lattice QCD with exact chiral symmetry

Abstract

Similarly to the interaction lagrangian, the possible boundary conditions in quantum field theories on space-time manifolds with boundaries are strongly constrained by the symmetry and scaling properties of the theory. Based on this general insight, a lattice formulation of the QCD Schrödinger functional is proposed for the case where the lattice Dirac operator in the bulk of the lattice coincides with the Neuberger--Dirac operator. The construction satisfies all basic requirements (locality, symmetries, hermiticity) and is suitable for numerical simulations.

arXiv commentPlain TeX source, 20 pages, no figures

References in corpus (20)

• Exactly massless quarks on the lattice
• Exact chiral symmetry on the lattice and the Ginsparg-Wilson relation
• More about exactly massless quarks on the lattice
• Chiral symmetry and O(a) improvement in lattice QCD
• The Schrödinger Functional - a Renormalizable Probe for Non-Abelian Gauge Theories
• The index theorem in QCD with a finite cut-off
• Locality properties of Neuberger's lattice Dirac operator
• The Theory of Boundary Critical Phenomena
• On the Schroedinger functional in QCD
• Lattice QCD without tuning, mixing and current renormalization
• O(a) improvement of the axial current in lattice QCD to one-loop order of perturbation theory
• Schwarz-preconditioned HMC algorithm for two-flavour lattice QCD
• Exact chiral symmetry, topological charge and related topics
• Prospects for perfect actions
• Numerical techniques for lattice QCD in the $\epsilon$--regime
• One-loop renormalization of the QCD Schrödinger functional
• Solution of the Dirac equation in lattice QCD using a domain decomposition method
• Localization properties of lattice fermions with plaquette and improved gauge actions
• Advanced Lattice QCD
• Schroedinger functional formalism with Ginsparg-Wilson fermion

Cited by in corpus (22)

• Lattice QCD with open boundary conditions and twisted-mass reweighting
• Lattice QCD without topology barriers
• The chirally rotated Schrödinger functional with Wilson fermions and automatic O(a) improvement
• Atiyah-Patodi-Singer index from the domain-wall fermion Dirac operator
• Introduction to Non-perturbative Heavy Quark Effective Theory
• Chiral Symmetry Restoration from a Boundary
• Non-perturbative renormalisation of left-left four-fermion operators with Neuberger fermions
• Atiyah-Patodi-Singer index on a lattice
• Schroedinger functional formalism with domain-wall fermion
• Why boundary conditions do not generally determine the universality class for boundary critical behavior
• A quenched study of the Schroedinger functional with chirally rotated boundary conditions: non-perturbative tuning
• A quenched study of the Schroedinger functional with chirally rotated boundary conditions: applications
• Restless pions: orbifold boundary conditions and noise suppression in lattice QCD
• A formulation of domain-wall fermions in the Schrödinger functional
• Non-perturbative renormalization in lattice QCD
• Perturbative analysis of the Neuberger-Dirac operator in the Schrödinger functional
• Lattice renormalisation of O(a) improved heavy-light operators
• Test of the Schrödinger functional with chiral fermions in the Gross-Neveu model
• $K$-theoretic computation of the Atiyah(-Patodi)-Singer index of lattice Dirac operators
• Rotational diffusion under torque: Microscopic reversibility and excess entropy
• Understanding the index theorems with massive fermions
• Construction of lattice Möbius domain wall fermions in the Schrödinger functional scheme