Some Consequences of the Hypothesis of Minimal Lengths

Talk presented at the 3rd International Symposium on Quantum Theory and Symmetries, September 13, 2003, University of Cincinnati, OH. Dedicated to the memory of Freydoon Mansouri.Comment: 8 pages, REVTeX

Superspace Dynamics and Perturbations Around "Emptiness"

Superspace parametrized by gauge potentials instead of metric three-geometries is discussed in the context of the Ashtekar variables. Among other things, an "internal clock" for the full theory can be identified. Gauge-fixing conditions which lead to the natural geometrical separation of physical from gauge modes are derived with the use of the metric in connection-superspace. A perturbation scheme about an unconventional background which is inaccessible to conventional variables is presented. The resultant expansion retains much of the simplicity of Ashtekar's formulation of General Relativity.Comment: 16 pages.(Revised 9/93) Preprint VPI-IHEP-93-5, CGPG-93/9-2, gr-qc/930701

The Gerasimov-Drell-Hearn Sum Rule and Current Algebras

The status of the Gerasimov-Drell-Hearn sum rules for polarized inclusive photo-production on nucleons is reviewed. It is shown that results from currently available data compare favorably with an estimate based on an extended current algebra. Implications for integrals of spin-dependent structure functions are also briefly discussed.Comment: 8 Page

Quantum Systems based upon Galois Fields: from Sub-quantum to Super-quantum Correlations

In this talk we describe our recent work on discrete quantum theory based on Galois fields. In particular, we discuss how discrete quantum theory sheds new light on the foundations of quantum theory and we review an explicit model of super-quantum correlations we have constructed in this context. We also discuss the larger questions of the origins and foundations of quantum theory, as well as the relevance of super-quantum theory for the quantum theory of gravity.Comment: 22 pages LaTeX. Uses ws-procs975x65.cls. Contribution to the Proceedings of the Conference in Honour of the 90th Birthday of Freeman Dyson, 26-29 August 2013, Institute of Advanced Studies at the Nanyang Technological University, Singapore. Talk presented by Takeuch