Bosonisation as The Hubbard-Stratonovich transformation

The problem of strongly correlated electrons in one dimension attracted attention of condensed matter physicists since early 50’s. After the seminal paper of Tomonaga [1] who suggested the first soluble model in 1950, there were essential achievements reflected in papers by Luttinger [2] (1963) and Mattis and Lieb [3] (1963). A considerable contribution to the understanding of generic properties of the 1D electron liquid has been made by Dzyaloshinskii and Larkin [4] (1973) and Efetov and Larkin [5] (1976). Despite the fact that the main features of the 1D electron liquid were captured and described by the end of 70’s, the investigators felt dissatisfied with the rigour of the theoretical description. The most famous example is the paper by Haldane [6] (1981) where the author developed the fundamentals of a modern bosonisation technique, known as the operator approach. This paper became famous because the author has rigourously shown how to construct the Fermi creation/anihilation operators out of the Bose ones. The most recent example of such a dissatisfaction is the review by von Delft and Schoeller [7] (1998) who revised the approach to the bosonisation and came up with what they called constructive bosonisation.

The Digital Observatory for Protected Areas (DOPA) Explorer 1.0

The Digital Observatory for Protected Areas (DOPA) has been developed to support the European Union’s efforts in strengthening our capacity to mobilize and use biodiversity data, information and forecasts so that they are readily accessible to policymakers, managers, experts and other users. Conceived as a set of web based services, DOPA provides a broad set of free and open source tools to assess, monitor and even forecast the state of and pressure on protected areas at local, regional and global scale. DOPA Explorer 1.0 is a web based interface available in four languages (EN, FR, ES, PT) providing simple means to explore the nearly 16,000 protected areas that are at least as large as 100 km2. Distinguishing between terrestrial, marine and mixed protected areas, DOPA Explorer 1.0 can help end users to identify those with most unique ecosystems and species, and assess the pressures they are exposed to because of human development. Recognized by the UN Convention on Biological Diversity (CBD) as a reference information system, DOPA Explorer is based on the best global data sets available and provides means to rank protected areas at the country and ecoregion levels. Inversely, DOPA Explorer indirectly highlights the protected areas for which information is incomplete. We finally invite the end-users of DOPA to engage with us through the proposed communication platforms to help improve our work to support the safeguarding of biodiversity.