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

Improved Lattice Actions with Chemical Potential

We give a prescription how to include a chemical potential \mu into a general lattice action. This inclusion does not cause any lattice artifacts. Hence its application to an improved - or even perfect - action at \mu =0 yields an improved resp. perfect action at arbitrary \mu. For short-ranged improved actions, a good scaling behavior holds over a wide region, and the upper bound for the baryon density - which is known for the standard lattice actions - can be exceeded.Comment: 7 pages, LaTex, 8 figures, talk presented at workshop on "QCD at Finite Baryon Density", Bielefeld, April 27-30, 199

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

Exact Supersymmetry on the Lattice

We discuss the possibility of representing supersymmetry exactly in a lattice discretized system. In particular, we construct a perfect supersymmetric action for the Wess-Zumino model.Comment: 9 pages, LaTex, no figure

Perfect Lattice Perturbation Theory: A Study of the Anharmonic Oscillator

As an application of perfect lattice perturbation theory, we construct an O(\lambda) perfect lattice action for the anharmonic oscillator analytically in momentum space. In coordinate space we obtain a set of 2-spin and 4-spin couplings \propto \lambda, which we evaluate for various masses. These couplings never involve variables separated by more than two lattice spacings. The O(\lambda) perfect action is simulated and compared to the standard action. We discuss the improvement for the first two energy gaps \Delta E_1, \Delta E_2 and for the scaling quantity \Delta E_2 / \Delta E1 in different regimes of the interaction parameter, and of the correlation length.Comment: LaTex, 27 pages, 9 figure