Properties of the Fixed Point Lattice Dirac Operator in the Schwinger Model

Abstract

We present a numerical study of the properties of the Fixed Point lattice Dirac operator in the Schwinger model. We verify the theoretical bounds on the spectrum, the existence of exact zero modes with definite chirality, and the Index Theorem. We show by explicit computation that it is possible to find an accurate approximation to the Fixed Point Dirac operator containing only very local couplings.

38 pages, LaTeX, 3 figures, uses style [epsfig], a few comments and relevant references added

References in corpus (4)

• Three topics in the Schwinger model
• The Perfect Quark-Gluon Vertex Function
• The Overlap Formalism and Topological Susceptibility on the Lattice
• SU(3) surface tension from the lattice with the fixed point action

Cited by in corpus (10)

• A new approach to Ginsparg-Wilson fermions
• Approximate Ginsparg-Wilson fermions: A first test
• Testing the fixed-point QCD action and the construction of chiral currents
• Topological Charge and The Spectrum of Exactly Massless Fermions on the Lattice
• Eigenvalue spectrum of massless Dirac operators on the lattice
• Convergence Rate and Locality of Improved Overlap Fermions
• New approximate solutions of the Ginsparg-Wilson equation - tests in 2-d
• Clover improvement, spectrum and Atiyah-Singer index theorem for the Dirac operator on the lattice
• Sum Rules for the Dirac Spectrum of the Schwinger Model
• Absence of evidence for pentaquarks on the lattice