An Adynamical, Graphical Approach to Quantum Gravity and Unification

We use graphical field gradients in an adynamical, background independent fashion to propose a new approach to quantum gravity and unification. Our proposed reconciliation of general relativity and quantum field theory is based on a modification of their graphical instantiations, i.e., Regge calculus and lattice gauge theory, respectively, which we assume are fundamental to their continuum counterparts. Accordingly, the fundamental structure is a graphical amalgam of space, time, and sources (in parlance of quantum field theory) called a "spacetimesource element." These are fundamental elements of space, time, and sources, not source elements in space and time. The transition amplitude for a spacetimesource element is computed using a path integral with discrete graphical action. The action for a spacetimesource element is constructed from a difference matrix K and source vector J on the graph, as in lattice gauge theory. K is constructed from graphical field gradients so that it contains a non-trivial null space and J is then restricted to the row space of K, so that it is divergence-free and represents a conserved exchange of energy-momentum. This construct of K and J represents an adynamical global constraint between sources, the spacetime metric, and the energy-momentum content of the element, rather than a dynamical law for time-evolved entities. We use this approach via modified Regge calculus to correct proper distance in the Einstein-deSitter cosmology model yielding a fit of the Union2 Compilation supernova data that matches LambdaCDM without having to invoke accelerating expansion or dark energy. A similar modification to lattice gauge theory results in an adynamical account of quantum interference.Comment: 47 pages text, 14 figures, revised per recent results, e.g., dark energy result

Lexicalization and Grammar Development

In this paper we present a fully lexicalized grammar formalism as a particularly attractive framework for the specification of natural language grammars. We discuss in detail Feature-based, Lexicalized Tree Adjoining Grammars (FB-LTAGs), a representative of the class of lexicalized grammars. We illustrate the advantages of lexicalized grammars in various contexts of natural language processing, ranging from wide-coverage grammar development to parsing and machine translation. We also present a method for compact and efficient representation of lexicalized trees.Comment: ps file. English w/ German abstract. 10 page

Quantum Field Theory

I discuss the general principles underlying quantum field theory, and attempt to identify its most profound consequences. The deepest of these consequences result from the infinite number of degrees of freedom invoked to implement locality. I mention a few of its most striking successes, both achieved and prospective. Possible limitations of quantum field theory are viewed in the light of its history.Comment: LaTeX, 12 pages, 3 figures. Will appear in Centenary issue of Rev. of Mod. Phys., March 1999. Incorporated minor corrections suggested by edito