On M-Theory

This contribution gives a personal view on recent attempts to find a unified framework for non-perturbative string theories, with special emphasis on the hidden symmetries of supergravity and their possible role in this endeavor. A reformulation of $d=11$ supergravity with enlarged tangent space symmetry SO(1,2) $\times$ SO(16) is discussed from this perspective, as well as an ansatz to construct yet further versions with SO(1,1) $\times$ SO(16)$^\infty$ and possibly even SO(1,1)$_+$ $\times$ ISO(16)$^\infty$ tangent space symmetry. It is suggested that upon ``third quantization'', dimensionally reduced maximal supergravity may have an equally important role to play in this unification as the dimensionally reduced maximally supersymmetric $SU(\infty)$ Yang Mills theory.Comment: 16 pages (Latex), contribution to the 31st Ahrenshoop International Symposium on the Theory of Elementary Particles, Buckow, Germany, 2-6 September 1997, and the Discussion Meeting on Black Holes, Bangalore, India, 8-10 December 1997. Changes in section 4, minor corrections in previous section

Extensions of supersymmetric spin systems

A discussion of supersymmetric spin systems is presented extending the results obtained in a recent paper (see ibid., vol.9, p.1497 (1976)). A two-dimensional model is given and gauge invariance is defined; the latter is shown to necessitate the introduction of further spin operators

Gravitational Billiards, Dualities and Hidden Symmetries

The purpose of this article is to highlight the fascinating, but only very incompletely understood relation between Einstein's theory and its generalizations on the one hand, and the theory of indefinite, and in particular hyperbolic, Kac Moody algebras on the other. The elucidation of this link could lead to yet another revolution in our understanding of Einstein's theory and attempts to quantize it.Comment: 37 pages, invited contribution to the volume "100 years of relativity spacetime structure: Einstein and beyond", ed. A. Ashteka

Reasonable fermionic quantum information theories require relativity

We show that any quantum information theory based on anticommuting operators must be supplemented by a superselection rule deeply rooted in relativity to establish a reasonable notion of entanglement. While quantum information may be encoded in the fermionic Fock space, the unrestricted theory has a peculiar feature: The marginals of bipartite pure states need not have identical entropies, which leads to an ambiguous definition of entanglement. We solve this problem, by proving that it is removed by relativity, i.e., by the parity superselection rule that arises from Lorentz invariance via the spin-statistics connection. Our results hence unveil a fundamental conceptual inseparability of quantum information and the causal structure of relativistic field theory.Comment: v2: 9 pages, 1 figure, expanded reference list and modified discussion, to appear in the New Journal of Physic