On Infravacua and the Localisation of Sectors

A certain class of superselection sectors of the free massless scalar field in 3 space dimensions is considered. It is shown that these sectors, which cannot be localised with respect to the vacuum, acquire a much better localisation, namely in spacelike cones, when viewed in front of suitable ``infravacuum'' backgrounds. These background states coincide, essentially, with a class of states introduced by Kraus, Polley and Reents as models for clouds of infrared radiation.Comment: LaTeX, 18 pages, minor corrections in order to conform with published versio

Bound states and the classical double copy

We extend the perturbative classical double copy to the analysis of bound systems. We first obtain the leading order perturbative gluon radiation field sourced by a system of interacting color charges in arbitrary time dependent orbits, and test its validity by taking relativistic bremsstrahlung and non-relativistic bound state limits. By generalizing the color to kinematic replacement rules recently used in the context of classical bremsstrahlung, we map the gluon emission amplitude to the radiation fields of dilaton gravity sourced by interacting particles in generic (self-consistent) orbits. As an application, we reproduce the leading post-Newtonian radiation fields and energy flux for point masses in non-relativistic orbits from the double copy of gauge theory.Comment: 9 pages, 1 figure, minor revisions to section II

On Infravacua and Superselection Theory

In the DHR theory of superselection sectors, one usually considers states which are local excitations of some vacuum state. Here, we extend this analysis to local excitations of a class of "infravacuum" states appearing in models with massless particles. We show that the corresponding superselection structure, the statistics of superselection sectors and the energy-momentum spectrum are the same as with respect to the vacuum state. (The latter result is obtained with a novel method of expressing the shape of the spectrum in terms of properties of local charge transfer cocycles.) These findings provide evidence to the effect that infravacua are a natural starting point for the analysis of the superselection structure in theories with long-range forces.Comment: LaTeX, 18 pages, spelling errors correcte

Baker domains for Newton's method

We show that there exists an entire function without finite asymptotic values for which the associated Newton function tends to infinity in some invariant domain. The question whether such a function exists had been raised by Douady.Comment: 8 page

Toward a unified PNT, Part 1: Complexity and context: Key challenges of multisensor positioning

The next generation of navigation and positioning systems must provide greater accuracy and reliability in a range of challenging environments to meet the needs of a variety of mission-critical applications. No single navigation technology is robust enough to meet these requirements on its own, so a multisensor solution is required. Known environmental features, such as signs, buildings, terrain height variation, and magnetic anomalies, may or may not be available for positioning. The system could be stationary, carried by a pedestrian, or on any type of land, sea, or air vehicle. Furthermore, for many applications, the environment and host behavior are subject to change. A multi-sensor solution is thus required. The expert knowledge problem is compounded by the fact that different modules in an integrated navigation system are often supplied by different organizations, who may be reluctant to share necessary design information if this is considered to be intellectual property that must be protected

Violating conformal invariance: Two-dimensional clusters grafted to wedges, cones, and branch points of Riemann surfaces

We present simulations of 2-d site animals on square and triangular lattices in non-trivial geomeLattice animals are one of the few critical models in statistical mechanics violating conformal invariance. We present here simulations of 2-d site animals on square and triangular lattices in non-trivial geometries. The simulations are done with the newly developed PERM algorithm which gives very precise estimates of the partition sum, yielding precise values for the entropic exponent $\theta$ ($Z_N \sim \mu^N N^{-\theta}$). In particular, we studied animals grafted to the tips of wedges with a wide range of angles $\alpha$, to the tips of cones (wedges with the sides glued together), and to branching points of Riemann surfaces. The latter can either have $k$ sheets and no boundary, generalizing in this way cones to angles $\alpha > 360$ degrees, or can have boundaries, generalizing wedges. We find conformal invariance behavior, $\theta \sim 1/\alpha$, only for small angles ($\alpha \ll 2\pi$), while $\theta \approx const -\alpha/2\pi$ for $\alpha \gg 2\pi$. These scalings hold both for wedges and cones. A heuristic (non-conformal) argument for the behavior at large $\alpha$ is given, and comparison is made with critical percolation.Comment: 4 pages, includes 3 figure