Europe: So Many Languages, So Many Cultures

The number of different languages in Europe by far exceeds the number of countries. All European countries have national languages, and in nearly all of them there are minority languages as well, whereas all major languages have dialects. National borders rarely coincide with linguistic borders, but the latter (including dialect borders) mark by their nature also more or less distinct cultural areas. This paper presents a survey of the different language families represented in Europe: Indo-European, Uralic, Altaic, and the four Caucasian language families, each with their sub-branches and individual languages. Some information is given on characteristic structural phenomena and on the status and history of these languages or language families and on some of their extinct predecessors. The paper ends with a short discussion on the language policy and practices of the institutions of the European Union. Europe lacks a language with the status and power comparable to Indonesian in Indonesia. The policy is therefore based on equal status of all national languages and on respect for all languages, including national minority ones. The practice, however, is unavoidably practical: “the more languages, the more English”

Loop formulation of the supersymmetric nonlinear O(N) sigma model

We derive the fermion loop formulation for the supersymmetric nonlinear O$(N)$ sigma model by performing a hopping expansion using Wilson fermions. In this formulation the fermionic contribution to the partition function becomes a sum over all possible closed non-oriented fermion loop configurations. The interaction between the bosonic and fermionic degrees of freedom is encoded in the constraints arising from the supersymmetry and induces flavour changing fermion loops. For $N \ge 3$ this leads to fermion loops which are no longer self-avoiding and hence to a potential sign problem. Since we use Wilson fermions the bare mass needs to be tuned to the chiral point. For $N=2$ we determine the critical point and present boson and fermion masses in the critical regime.Comment: 7 pages, 4 figures, presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, German

Loop formulation of supersymmetric Yang-Mills quantum mechanics

We derive the fermion loop formulation of N=4 supersymmetric SU(N) Yang-Mills quantum mechanics on the lattice. The loop formulation naturally separates the contributions to the partition function into its bosonic and fermionic parts with fixed fermion number and provides a way to control potential fermion sign problems arising in numerical simulations of the theory. Furthermore, we present a reduced fermion matrix determinant which allows the projection into the canonical sectors of the theory and hence constitutes an alternative approach to simulate the theory on the lattice.Comment: 20 pages, 3 figure

Supersymmetry breaking on the lattice: the N=1 Wess-Zumino model

We discuss spontaneous supersymmetry breaking in the N=1 Wess-Zumino model in two dimensions on the lattice using Wilson fermions and the fermion loop formulation. In that formulation the fermion sign problem related to the vanishing of the Witten index can be circumvented and the model can be simulated very efficiently using the recently introduced open fermion string algorithm. We present first results for the supersymmetry breaking phase transition and sketch the preliminary determination of a renormalised critical coupling in the continuum limit.Comment: 7 pages, 4 figures, proceedings of the XXIX International Symposium on Lattice Field Theory - Lattice 2011, July 10-16, 2011, Squaw Valley, Lake Tahoe, Californi