Localizing the Relativistic Electron

A causally well-behaved solution of the localization problem for the free electron is given, with natural space-time transformation properties, in terms of Dirac's position operator. It is shown that, although this operator does not represent an observable in the usual sense, and has no positive-energy (generalized) eigenstates, the associated 4-vector density is observable, and can be localized arbitrarily precisely about any point in space, at any instant of time, using only positive-energy states. A suitable spin operator can be diagonalized at the same time.Comment: 19 pages including 1 figure (1 LatTex2e file, 1 postscript file). Uses package amssymb. Typos correcte

Waiting for the quantum bus: the flow of negative probability

It is 45 years since the discovery of the peculiar quantum effect known as ‘probability backflow’, and it is 20 years since the greatest possible size of the effect was characterized. Recently an experiment has been proposed to observe it directly, for the first time, by manipulating ultra-cold atoms. Here a non-technical description is given of the effect and its interpretation in terms of the flow of negative probability

Fusarium crown rot under continuous cropping of susceptible and partially resistant wheat in microcosms at elevated CO2

This study examines the CO2-mediated influence of plant resistance on crown rot dynamics under continuous cropping of partially resistant wheat line 249 and the susceptible cultivar Tamaroi. Disease incidence, severity, deoxynivalenol and Fusarium biomass were assessed after each cycle in microcosms established at ambient and 700mgkg(-1) CO2 using soil and stubble of these wheat lines from a field experiment with free to air CO2 enrichment. Monoconidial isolates from wheat stubble were collected initially, and after five cropping cycles, to compare the frequency and aggressiveness of Fusarium species in the two populations. Aggressiveness was measured using a high-throughput seedling bioassay. At elevated CO2, the higher initial incidence in Tamaroi increased with cropping cycles, but incidence in 249 remained unchanged. Incidence at ambient CO2 did not change for either line. Elevated CO2 induced partial resistance in Tamaroi, but not in 249. Increased Fusarium biomass in wheat tissue at elevated CO2 matched raised deoxynivalenol of the stem base in both lines. After five cycles of continuous wheat cropping, aggressiveness increased in pathogenic F.culmorum and F.pseudograminearum by 110%, but decreased in weakly pathogenic F.equiseti and F.oxysporum by 50%. CO2 and host resistance interactively influenced species frequency, and the highly aggressive F.pseudograminearum became dominant on Tamaroi irrespective of CO2 concentration, while its frequency declined on 249. This study shows that induced resistance at elevated CO2 will not reduce crown rot severity, or impede the selection and enrichment of Fusarium populations with increased aggressiveness