Poisson sigma models and deformation quantization

This is a review aimed at a physics audience on the relation between Poisson sigma models on surfaces with boundary and deformation quantization. These models are topological open string theories. In the classical Hamiltonian approach, we describe the reduced phase space and its structures (symplectic groupoid), explaining in particular the classical origin of the non-commutativity of the string end-point coordinates. We also review the perturbative Lagrangian approach and its connection with Kontsevich's star product. Finally we comment on the relation between the two approaches.Comment: 11 page

On the AKSZ formulation of the Poisson sigma model

We review and extend the Alexandrov-Kontsevich-Schwarz-Zaboronsky construction of solutions of the Batalin-Vilkovisky classical master equation. In particular, we study the case of sigma models on manifolds with boundary. We show that a special case of this construction yields the Batalin-Vilkovisky action functional of the Poisson sigma model on a disk. As we have shown in a previous paper, the perturbative quantization of this model is related to Kontsevich's deformation quantization of Poisson manifolds and to his formality theorem. We also discuss the action of diffeomorphisms of the target manifolds.Comment: 19 page

A path integral approach to the Kontsevich quantization formula

We give a quantum field theory interpretation of Kontsevich's deformation quantization formula for Poisson manifolds. We show that it is given by the perturbative expansion of the path integral of a simple topological bosonic open string theory. Its Batalin-Vilkovisky quantization yields a superconformal field theory. The associativity of the star product, and more generally the formality conjecture can then be understood by field theory methods. As an application, we compute the center of the deformed algebra in terms of the center of the Poisson algebra.Comment: 22 pages, 2 figures, references added. Conjecture on the center made more precis

From local to global deformation quantization of Poisson manifolds

We give an explicit construction of a deformation quantization of the algebra of functions on a Poisson manifolds, based on Kontsevich's local formula. The deformed algebra of functions is realized as the algebra of horizontal sections of a vector bundle with flat connection.Comment: 16 pages. Reference and dedication added. Sign corrected, remark on Poisson vector fields adde

Fedosov connections on jet bundles and deformation quantization

We review our construction of star-products on Poisson manifolds and discuss some examples. In particular, we work out the relation with Fedosov's original construction in the symplectic case.Comment: Contribution to the proceedings of the conference "Deformation Quantization", Strasbourg, May 31-June 2, 200

Elliptic quantum groups and Ruijsenaars models

We construct symmetric and exterior powers of the vector representation of the elliptic quantum groups $E_{\tau,\eta}(gl_N)$. The corresponding transfer matrices give rise to various integrable difference equations which could be solved in principle by the nested Bethe ansatz method. In special cases we recover the Ruijsenaars systems of commuting difference operators.Comment: 15 pages, late

Gesundheitsausgaben und demografischer Wandel

Zusammenfassung: Der Einfluss steigender Lebenserwartung auf die künftigen Gesundheitsausgaben wird aufgrund einer immer stärker ins hohe Alter verdrängten Mortalität einerseits und hoher Gesundheitsausgaben im letzten Lebensjahr (sogenannte Sterbekosten) andererseits moderat ausfallen. Da der Anstieg der individuellen Krankheitsausgaben nicht durch das Alter an sich, sondern durch die hohen Kosten in der Nähe zum Tod verursacht wird, hat der Aufschub der Mortalität in höhere Alter keinen starken Effekt auf die Lebensausgaben für Gesundheit. Eine Schätzung der GKV-Ausgabenentwicklung bis 2050, die die Sterbekosten explizit berücksichtigt, legt einen geringeren demografischen Einfluss nahe als eine Prognose auf Grundlage gegebener altersspezifischer Gesundheitsausgabenprofil

Parafermionic theory with the symmetry Z_N, for N even

Following our previous papers (hep-th/0212158 and hep-th/0303126) we complete the construction of the parafermionic theory with the symmetry Z_N based on the second solution of Fateev-Zamolodchikov for the corresponding parafermionic chiral algebra. In the present paper we construct the Z_N parafermionic theory for N even. Primary operators are classified according to their transformation properties under the dihedral group (Z_N x Z_2, where Z_2 stands for the Z_N charge conjugation), as two singlets, doublet 1,2,...,N/2-1, and a disorder operator. In an assumed Coulomb gas scenario, the corresponding vertex operators are accommodated by the Kac table based on the weight lattice of the Lie algebra D_{N/2}. The unitary theories are representations of the coset SO_n(N) x SO_2(N) / SO_{n+2}(N), with n=1,2,.... We suggest that physically they realise the series of multicritical points in statistical systems having a Z_N symmetry

Regional convergence and economic performance: a case study of the West German Laender

In the paper we analyze the convergence process of the West German Laender from 1970 to 1995 using descriptive tools as well as panel estimation methods. Although there have been some winners in this process, the main finding is that convergence was insufficient in the sense that no gains have been achieved with respect to a stronger harmonization of the economic performances in the Laender. Some of them proofed to be unable to respond adequately to structural changes, whereas others successfully overcame those challenges. Panel estimates of production functions of the Laender reveal no significant differences in the production technology across Laender. -- Die Arbeit untersucht, ob im Zeitraum von 1970 bis 1996 eine Konvergenz im wirtschaftlichen Wachstum der westlichen Bundesländer stattgefunden hat. Die Ergebnisse zeigen, daß insbesondere die südlichen Bundesländer ihre relative Position verbessern konnten. Jene Bundesländer, die schon 1970 als ?strukturschwach? galten, schafften es nicht, den Abstand zu verringern. Der Strukturwandel wurde von den einzelnen Bundesländern mit unterschiedlichem Erfolg bewältigt. Eine Länder vermochten daraus Vorteile für ihre Entwicklung zu ziehen, während andere nur unzureichend auf diese Herausforderung reagierten. Insgesamt kann im Untersuchungszeitraum weder von einer Konvergenz noch von einer Divergenz der wirtschaftlichen Entwicklung in den Ländern gesprochen werden. Dem widerspricht nicht, daß einige Ländern (Hessen und Bayern) insgesamt erfolgreicher in ihrer Entwicklung waren als die übrigen Bundesländer.

Parafermionic theory with the symmetry Z_N, for N odd

We construct a parafermionic conformal theory with the symmetry Z_N, for N odd, based on the second solution of Fateev-Zamolodchikov for the corresponding parafermionic chiral algebra. Primary operators are classified according to their transformation properties under the dihedral group D_N, as singlet, doublet 1,2,...,(N-1)/2, and disorder operators. In an assumed Coulomb gas scenario, the corresponding vertex operators are accommodated by the weight lattice of the Lie algebra B_(N-1)/2. The unitary theories are representations of the coset SO_n(N) x SO_2(N) / SO_{n+2}(N), with n=1,2,... . Physically, they realise the series of multicritical points in statistical theories having a D_N symmetry.Comment: 34 pages, 1 figure. v2: note added in proo