Titlebook: Geometry and Quantum Physics; Proceedings of the 3 H. Gausterer,L. Pittner,Harald Grosse Conference proceedings 2000 Springer-Verlag Berlin

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A. Nippoldt,J. Keränen,E. SchweidlerWe present a global path integral density for the Yang-Mills theory by summing over all partitions of the space of gauge potentials.

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T-Duality and the Gravitational Description of Gauge Theories,This is a review of some basic features on the relation between su- pergravity and pure gauge theories with special emphasis on the relation between T-duality and supersymmetry. Some new results concerning the interplay between T-duality and near horizon geometries are presented.

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An Introduction to Noncommutative Geometry,A review is made of some recent results in noncommutative geometry, including its use as a regularization procedure. Efforts to add a gravitational field to noncommutative models of space-time are also reviewed. Special emphasis is placed on the case which could be considered as the noncommutative analogue of a parallelizable space-time.

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A Quantum Minkowski Space-Time,The representation theory of a .-deformed Minkowski algebra, which is as quantum space a co-module of the .-Poincaré algebra, is studied. The spectra of the coordinates are discrete: space-time acquires a lattice-like structure. The eigenvalues grow exponentially and there are accumulation points on the light-cone.

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Supersymmetry and Nonperturbative Aspects in Quantum Cosmology,The important question of the modern superstring and M - theories is the problem of the spontaneous breakdown of the supersymmetry. We consider the dynamical (nonperturbative) breaking of supersymmetry, caused by gravitational and Yang-Mills (YM) instantons in quantum cosmology.

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Absolute Conservation Law for Black Holes,The spherically reduction of the 4d Einstein-Hilbert action reduces to a 2d dilaton theory[.], which can be shown to be equivalent to a first order action (with nonvanishing torsion)[.] being a special case of a Poisson-σ model[.].

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https://doi.org/10.1007/978-3-642-96680-4antum Regge calculus. The Standard Regge Calculus [.] where the quadratic link lengths q of the simplicial manifold vary continuously and the Discrete Regge Model [.] where they are restricted to two possible values. These manifolds are coupled with Z. spins [.].

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