Quantization and the Issue of Time for Various Two-Dimensional Models of Gravity

It is shown that the models of 2D Liouville Gravity, 2D Black Hole- and $R^2$-Gravity are {\em embedded} in the Katanaev-Volovich model of 2D NonEinsteinian Gravity. Different approaches to the formulation of a quantum theory for the above systems are then presented: The Dirac constraints can be solved exactly in the momentum representation, the path integral can be integrated out, and the constraint algebra can be {\em explicitely} canonically abelianized, thus allowing also for a (superficial) reduced phase space quantization. Non--trivial dynamics are obtained by means of time dependent gauges. All of these approaches lead to the {\em same} finite dimensional quantum mechanical system.Comment: 4 pages, LaTeX, Talk given at the Journ\'ees Relativistes '93, TUW930

All Symmetries of Non-Einsteinian Gravity in d=2d =2

The covariant form of the field equations for two--dimensional $R^2$--gravity with torsion as well as its Hamiltonian formulation are shown to suggest the choice of the light--cone gauge. Further a one--to--one correspondence between the Hamiltonian gauge symmetries and the diffeomorphisms and local Lorentz transformations is established, thus proving that there are no hidden local symmetries responsible for the complete integrability of the model. Finally the constraint algebra is shown to have no quantum anomalies so that Dirac's quantization should be applicable.Comment: LaTex, 16 pages, TUW9207, (Some smaller corrections, cross-references updated

Weak Arithmetical Interpretations for the Logic of Proofs

Artemov established an arithmetical interpretation for the Logics of Proofs LPCS, which yields a classical provability semantics for the modal logic S4. These Logics of Proofs are parameterized by so-called constant specifications CS that state which axioms can be used in the reasoning process, and the arithmetical interpretation relies on the constant specifications being finite. In this paper, we remove this restriction by introducing weak arithmetical interpretations that are sound and complete for a wide class of constant specifications, including infinite ones. In particular, they interpret the full Logic of Proofs LP. Keywords: Logic of Proofs, arithmetical interpretation, BHK semantic

Improving the Efficiency of FP-LAPW Calculations

The full-potential linearized augmented-plane wave (FP-LAPW) method is well known to enable most accurate calculations of the electronic structure and magnetic properties of crystals and surfaces. The implementation of atomic forces has greatly increased it's applicability, but it is still generally believed that FP-LAPW calculations require substantial higher computational effort compared to the pseudopotential plane wave (PPW) based methods. In the present paper we analyse the FP-LAPW method from a computational point of view. Starting from an existing implementation (WIEN95 code), we identified the time consuming parts and show how some of them can be formulated more efficiently. In this context also the hardware architecture plays a crucial role. The remaining computational effort is mainly determined by the setup and diagonalization of the Hamiltonian matrix. For the latter, two different iterative schemes are compared. The speed-up gained by these optimizations is compared to the runtime of the ``original'' version of the code, and the PPW approach. We expect that the strategies described here, can also be used to speed up other computer codes, where similar tasks must be performed.Comment: 20 pages, 3 figures. Appears in Comp. Phys. Com. Other related publications can be found at http://www.rz-berlin.mpg.de/th/paper.htm

Citizen Humanities as a Fusion of Digital and Public Humanities?

Digital and public humanities have gained a foothold in academia, but very little is known about citizen humanities, which is referring to the engagement of the general public in scholarly research. Although the term is new, public participation in the humanities, either as the citizens’ contribution of intellectual effort or knowledge to academic research, or as the contribution of resources and tools, looks back on a long tradition. The citizen humanities range from the creation of dictionaries, the transcription and annotation of historical records to the decoding of ancient Egyptian papyri. While the digital humanities provide the citizen humanities with data, tools and techniques, the public humanities offer the means of engaging diverse publics in research activities. After embedding the citizen humanities theoretically in the responsible research and innovation paradigm, this paper will illustrate how digitisation and public involvement laid the foundations for today’s citizen humanities. With a focus on the fusion of digital and public humanities in citizen humanities, this paper will demonstrate the mutual influence on practices (of research). This influence is not only reflected in the approaches to research, analysis, communication, and dissemination but also in the citizen humanities’ novel ways of knowledge co-production