Perfect Actions for Scalar Theories

We construct an optimally local perfect lattice action for free scalars of arbitrary mass, and truncate its couplings to a unit hypercube. Spectral and thermodynamic properties of this ``hypercube scalar'' are drastically improved compared to the standard action. We also discuss new variants of perfect actions, using anisotropic or triangular lattices, or applying new types of RGTs. Finally we add a \lambda \phi^4 term and address perfect lattice perturbation theory. We report on a lattice action for the anharmonic oscillator, which is perfect to O(\lambda).Comment: 3 pages, LaTex, 4 figures, talk presented at LATTICE'97, Ref. [1] correcte

The Photon Dispersion as an Indicator for New Physics ?

We first comment on the search for a deviation from the linear photon dispersion relation, in particular based on cosmic photons from Gamma Ray Bursts. Then we consider the non-commutative space as a theoretical concept that could lead to such a deviation, which would be a manifestation of Lorentz Invariance Violation. In particular we review a numerical study of pure U(1) gauge theory in a 4d non-commutative space. Starting from a finite lattice, we explore the phase diagram and the extrapolation to the continuum and infinite volume. These simultaneous limits - taken at fixed non-commutativity - lead to a phase of broken Poincare symmetry, where the photon appears to be IR stable, despite a negative IR divergence to one loop.Comment: 8 pages, 4 figures, talk presented at the VI International Workshop on the Dark Side of the Universe, Leon (Mexico), June 1-6, 2010. References adde

Solutions of the Ginsparg-Wilson relation and improved domain wall fermions

We discuss a number of lattice fermion actions solving the Ginsparg-Wilson relation. We also consider short ranged approximate solutions. In particular, we are interested in reducing the lattice artifacts, while avoiding (or suppressing) additive mass renormalization. In this context, we also arrive at a formulation of improved domain wall fermions.Comment: 20 pages LaTex, 3 double figures, 4 tables, final version to appear in Eur. Phys. J.

Overlap Hypercube Fermions in QCD

We present simulation results obtained with overlap hypercube fermions in QCD near the chiral limit. We relate our results to chiral perturbation theory in both, the epsilon-regime and in the p-regime. In particular we measured the pion decay constant by different methods, as well as the chiral condensate, light meson masses, the PCAC quark mass and the renormalisation constant Z_A.Comment: 8 pages, 9 figures, talk presented at Workshop on Computational Hadron Physics, Nicosia, Cyprus, Sept. 14-17, 200

Convergence Rate and Locality of Improved Overlap Fermions

We construct new Ginsparg-Wilson fermions for QCD by inserting an approximately chiral Dirac operator - which involves ingredients of a perfect action - into the overlap formula. This accelerates the convergence of the overlap Dirac operator by a factor of 5 compared to the standard construction, which inserts the Wilson fermion as a point of departure. Taking into account the effort for treating the improved fermion, we are left with an total computational overhead of about a factor 3. This remaining factor is likely to be compensated by other virtues; here we show that the level of locality is clearly improved, so that the exponent of the correlation decay is doubled. We also show that approximate rotation invariance is drastically improved, but a careful scaling test has to be postponed.Comment: 33 pages, 16 figures, a Section on approximate rotation symmetry is adde