Scheme Independence to all Loops

The immense freedom in the construction of Exact Renormalization Groups means that the many non-universal details of the formalism need never be exactly specified, instead satisfying only general constraints. In the context of a manifestly gauge invariant Exact Renormalization Group for SU(N) Yang-Mills, we outline a proof that, to all orders in perturbation theory, all explicit dependence of beta function coefficients on both the seed action and details of the covariantization cancels out. Further, we speculate that, within the infinite number of renormalization schemes implicit within our approach, the perturbative beta function depends only on the universal details of the setup, to all orders.Comment: 18 pages, 8 figures; Proceedings of Renormalization Group 2005, Helsinki, Finland, 30th August - 3 September 2005. v2: Published in jphysa; minor changes / refinements; refs. adde

Sensitivity of Nonrenormalizable Trajectories to the Bare Scale

Working in scalar field theory, we consider RG trajectories which correspond to nonrenormalizable theories, in the Wilsonian sense. An interesting question to ask of such trajectories is, given some fixed starting point in parameter space, how the effective action at the effective scale, Lambda, changes as the bare scale (and hence the duration of the flow down to Lambda) is changed. When the effective action satisfies Polchinski's version of the Exact Renormalization Group equation, we prove, directly from the path integral, that the dependence of the effective action on the bare scale, keeping the interaction part of the bare action fixed, is given by an equation of the same form as the Polchinski equation but with a kernel of the opposite sign. We then investigate whether similar equations exist for various generalizations of the Polchinski equation. Using nonperturbative, diagrammatic arguments we find that an action can always be constructed which satisfies the Polchinski-like equation under variation of the bare scale. For the family of flow equations in which the field is renormalized, but the blocking functional is the simplest allowed, this action is essentially identified with the effective action at Lambda = 0. This does not seem to hold for more elaborate generalizations.Comment: v1: 23 pages, 5 figures, v2: intro extended, refs added, published in jphy

Multi-Frequency Synthesis of VLBI Images Using a Generalized Maximum Entropy Method

A new multi-frequency synthesis algorithm for reconstructing images from multi-frequency VLBI data is proposed. The algorithm is based on a generalized maximum-entropy method, and makes it possible to derive an effective spectral correction for images over a broad frequency bandwidth, while simultaneously reconstructing the spectral-index distribution over the source. The results of numerical simulations demonstrating the capabilities of the algorithm are presented.Comment: 17 pages, 8 figure

Evidence for bimodal orbital separations of white dwarf-red dwarf binary stars

We present the results of a radial velocity survey of 20 white dwarf plus M dwarf binaries selected as a follow up to a \textit{Hubble Space Telescope} study that aimed to spatially resolve suspected binaries. Our candidates are taken from the list of targets that were spatially unresolved with \textit{Hubble}. We have determined the orbital periods for 16 of these compact binary candidates. The period distribution ranges from 0.14 to 9.16\,d and peaks near 0.6\,d. The original sample therefore contains two sets of binaries, wide orbits ($\approx100-1000$\,au) and close orbits ($\lesssim1-10$\,au), with no systems found in the $\approx10-100$\,au range. This observational evidence confirms the bimodal distribution predicted by population models and is also similar to results obtained in previous studies. We find no binary periods in the months to years range, supporting the post common envelope evolution scenario. One of our targets, WD\,1504+546, was discovered to be an eclipsing binary with a period of 0.93\,d