Spontaneous edge currents are known to occur in systems of two space dimensions in a strong magnetic field. The latter creates chirality and determines the direction of the currents. Here we show that an analogous effect occurs in a field-free situation when time reversal symmetry is broken by the mass term of the Dirac equation in two space dimensions. On a half plane, one sees explicitly that the strength of the edge current is proportional to the difference between the chemical potentials at the edge and in the bulk, so that the effect is analogous to the Hall effect, but with an internal potential. The edge conductivity differs from the bulk (Hall) conductivity on the whole plane. This results from the dependence of the edge conductivity on the choice of a selfadjoint extension of the Dirac Hamiltonian. The invariance of the edge conductivity with respect to small perturbations is studied in this example by topological techniques.
The partition function of rational conformal field theories (CFTs) on Riemann surfaces is expected to satisfy ODEs of Gauss-Manin type. We investigate the case of hyperelliptic surfaces and derive the ODE system for the (2, 5) minimal model.Abusing notations, we shall simply write ϕ(z) where we actually mean ϕ z (p). (This will entail notations like φ(ẑ) instead of ϕ ẑ( p) etc.)We shall only consider bundles that lie in |Vec(F)|. Primary fieldsLet O C be the sheaf of germs U, f which are represented by pairs (U, f ) for some open set U ⊆ C and some conformal map f : U → C. Let O C,0 be the fiber of germs in O C which are defined at the origin in C, and letIt is easy to see that G is a group under pointwise composition, with identity element C, id . G is actually a Lie group [15, p. 267]. G is a real manifold that admits no complexification.The Lie algebra g of G can be identified with the Lie algebra of germs of holomorphic vector fields on C which vanish at the origin [3],
Background Treating patients with inflammatory joint diseases (rheumatoid arthritis, psoriatic arthritis) according to established treatment algorithms often requires the simultaneous use of three or more medications to relieve symptoms and prevent long-term joint damage as well as disability. Objective To assess and give an overview on drug-drug interactions in the pharmacotherapy of inflammatory joint diseases with regards to their clinical relevance. Methods All possible drug combinations were evaluated using three commercially available drug interaction programs. In those cases where only limited/no data were found, a comprehensive hand search of Pubmed was carried out. Finally, the drug-drug interactions of all possible combinations were classified according to evidence-based medicine and a specifically generated relevance-based system. Results All three interaction software programs showed consistent results. All detected interactions were combined in clearly structured tables. Conclusion A concise overview on drug-drug interactions is given. Especially in more sophisticated cases extensive knowledge of drug interactions supports optimisation of therapy and results in improved patient safety.
This is an abstract of the PhD thesis CFTs on Riemann Surfaces of genus g ≥ 1 in mathematics, written by Dr. Marianne Leitner under the supervision of Prof. Dmitri Zaitsev at the School of Mathematics, TCD, and submitted in August 2013.The purpose of this thesis is to argue that N -point functions of holomorphic fields in rational conformal field theories can be calculated by methods from algebraic geometry. We establish explicit formulae for the 2-point function of the Virasoro field on hyperelliptic Riemann surfaces of genus g ≥ 1. N -point functions for higher N are obtained inductively, and we show that they have a nice graphical representation. We discuss the Virasoro 3-point function with application to the Virasoro (2, 5) minimal model.The formulae involve a finite number of parameters, notably the 0-point function and the Virasoro 1-point function, which depend on the moduli of the surface and can be calculated by differential equations. We propose an algebraic geometric approach that applies to any hyperelliptic Riemann surface. Our discussion includes a demonstration of our methods to the case g = 1.
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