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

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

Improving the locality of the overlap Dirac operator via approximate solutions of the Ginsparg-Wilson relation

We determine the free field hypercubic Dirac operator which is optimally close to satisfying the Ginsparg-Wilson relation. Inserting this operator into the overlap formula, we show that the analytic locality bound on the resulting overlap Dirac operator is substantially stronger than in the standard case. This improvement generally persists in gauge backgrounds when the plaquette variables are all close to unity.Comment: 3 pages, contributed to Proceedings of Lattice2003(chiral

A fixed-point action for the lattice Schwinger model

We determine non-perturbatively a fixed-point (FP) action for fermions in the two-dimensional U(1) gauge (Schwinger) model. Our parameterization for the fermionic action has terms within a $7\times 7$ square on the lattice, using compact link variables. With the Wilson fermion action as starting point we determine the FP-action by iterating a block spin transformation (BST) with a blocking factor of 2 in the background of non-compact gauge field configurations sampled according to the (perfect) Gaussian measure. We simulate the model at various values of $\beta$ and find excellent improvement for the studied observables.Comment: 3 pages (LaTeX), 2 figures (EPS

VLBI Observations of SN 2008D

We report on two epochs of very-long-baseline interferometry (VLBI) observations of the Type Ib/c supernova SN 2008D, which was associated with the X-ray outburst XRF 080109. At our first epoch, at t = 30 days after the explosion, we observed at 22 and 8.4 GHz, and at our second, at t = 133 days, at 8.4 and 5.0 GHz. The VLBI observations allow us to accurately measure the source's size and position at each epoch, and thus constrain its expansion velocity and proper motion. We find the source at best marginally resolved at both epochs, allowing us to place a 3sigma upper limit of ~0.75c on the expansion velocity of a circular source. For an elongated source, our measurements are compatible with mildly relativistic expansion. However, our 3sigma upper limit on the proper motion is 4 micro-arcsec/day, corresponding to an apparent velocity of <0.6c, and is consistent with a stationary flux centroid. This limit rules out a relativistic jet such as an gamma-ray burst jet away from the line of sight, which would be expected to show apparent proper motion of >c. Taken together, our measurements argue against the presence of any long-lived relativistic outflow in SN 2008D. On the other hand, our measurements are consistent with the nonrelativistic expansion velocities of <30,000 km/s and small proper motions (<500 km/s) seen in typical supernovae.Comment: Accepted for publication in the Astrophysical Journal Letter

The Perfect Laplace Operator for Non-Trivial Boundaries

The application of Renormalization Group (RG) methods to find perfect discretizations of partial differential equations is a promising but little investigated approach. We calculate the classically perfect fixed-point Laplace operator for boundaries of non-trivial shape analytically and numerically and present a parametrization that can be used for solving the Poisson equation.Comment: Poster for Lattice 2000 (Improvement), 5 page

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

Progress on Perfect Lattice Actions for QCD

We describe a number of aspects in our attempt to construct an approximately perfect lattice action for QCD. Free quarks are made optimally local on the whole renormalized trajectory and their couplings are then truncated by imposing 3-periodicity. The spectra of these short ranged fermions are excellent approximations to continuum spectra. The same is true for free gluons. We evaluate the corresponding perfect quark-gluon vertex function, identifying in particular the ``perfect clover term''. First simulations for heavy quarks show that the mass is strongly renormalized, but again the renormalized theory agrees very well with continuum physics. Furthermore we describe the multigrid formulation for the non-perturbative perfect action and we present the concept of an exactly (quantum) perfect topological charge on the lattice.Comment: 14 pages, 17 figures, Talk presented at LATTICE96(improvement

The Crab Nebula at 1.3 mm: evidence for a new synchrotron component

We present the results of 1.3 mm observations of the Crab Nebula, performed with the MPIfR bolometer arrays at the IRAM 30-m telescope. The maps obtained, of unprecedented quality at these wavelengths, allow a direct comparison with high-resolution radio maps. Although the spatial structure of the Crab Nebula does not change much from radio to millimetre wavelengths, we have detected significant spatial variations of the spectral index between 20 cm and 1.3 mm. The main effect is a spectral flattening in the inner region, which can be hardly explained just in terms of the evolution of a single population of synchrotron emitting electrons. We propose instead that this is the result of the emergence of a second synchrotron component, that we have tried to extract from the data. Shape and size of this component resemble those of the Crab Nebula in X rays. However, while the more compact structure of the Crab Nebula in X rays is commonly regarded as an effect of synchrotron downgrading, it cannot be explained why a similar structure is present also at mm wavelengths, where the electron lifetimes far exceed the nebular age. Our data, combined with published upper limits on spatial variations of the radio spectral index, also imply a low-energy cutoff for the distribution of electrons responsible for this additional synchrotron component. Although no model has been developed so far to explain the details of this component, one may verify that the total number of the electrons responsible for it is in agreement with what predicted by the classical pulsar-wind models, which otherwise are known to fail in accounting for the number of radio emitting electrons. We have also detected a spectral steepening at mm wavelengths in some elongated regions, whose positions match those of radio synchrotron filaments.Comment: 10 pages, Latex, 8 figures, JPEG, given separately Submitted to Astronomy and Astrophysic