Classical and Quantum Implications of the Causality Structure of Two-Dimensional Spacetimes with Degenerate Metrics

The causality structure of two-dimensional manifolds with degenerate metrics is analysed in terms of global solutions of the massless wave equation. Certain novel features emerge. Despite the absence of a traditional Lorentzian Cauchy surface on manifolds with a Euclidean domain it is possible to uniquely determine a global solution (if it exists), satisfying well defined matching conditions at the degeneracy curve, from Cauchy data on certain spacelike curves in the Lorentzian region. In general, however, no global solution satisfying such matching conditions will be consistent with this data. Attention is drawn to a number of obstructions that arise prohibiting the construction of a bounded operator connecting asymptotic single particle states. The implications of these results for the existence of a unitary quantum field theory are discussed.Comment: 27 pages LaTex (6 Figures), Journal of Mathematical Physics (Accepted

Gauge Symmetry and Gravito-Electromagnetism

A tensor description of perturbative Einsteinian gravity about an arbitrary background spacetime is developed. By analogy with the covariant laws of electromagnetism in spacetime, gravito-electromagnetic potentials and fields are defined to emulate electromagnetic gauge transformations under substitutions belonging to the gauge symmetry group of perturbative gravitation. These definitions have the advantage that on a flat background, with the aid of a covariantly constant timelike vector field, a subset of the linearised gravitational field equations can be written in a form that is fully analogous to Maxwell's equations (without awkward factors of 4 and extraneous tensor fields). It is shown how the remaining equations in the perturbed gravitational system restrict the time dependence of solutions to these equations and thereby prohibit the existence of propagating vector fields. The induced gravito-electromagnetic Lorentz force on a test particle is evaluated in terms of these fields together with the torque on a small gyroscope. It is concluded that the analogy of perturbative gravity to Maxwell's description of electromagnetism can be valuable for (quasi-)stationary gravitational phenomena but that the analogy has its limitations.Comment: 29 pages no-fig

An Interview With Albert W. Tucker

The mathematical career of Albert W. Tucker, Professor Emeritus at Princeton University, spans more than 50 years. Best known today for his work in mathematical programming and the theory of games (e.g., the Kuhn-Tucker theorem, Tucker tableaux, and the Prisoner\u27s Dilemma), he was also in his earlier years prominent in topology. Outstanding teacher, administrator and leader, he has been President of the MAA, Chairman of the Princeton Mathematics Department, and course instructor, thesis advisor or general mentor to scores of active mathematicians. He is also known for his views on mathematics education and the proper interplay between teaching and research. Tucker took an active interest in this interview, helping with both the planning and the editing. The interviewer, Professor Maurer, received his Ph.D. under Tucker in 1972 and teaches at Swarthmore College

An Intrinsic Approach to Forces in Magnetoelectric Media

This paper offers a conceptually straightforward method for the calculation of stresses in polarisable media based on the notion of a drive form and its property of being closed in spacetimes with symmetry. After an outline of the notation required to exploit the powerful exterior calculus of differential forms, a discussion of the relation between Killing isometries and conservation laws for smooth and distributional drive forms is given. Instantaneous forces on isolated spacetime domains and regions with interfaces are defined, based on manifestly covariant equations of motion. The remaining sections apply these notions to media that sustain electromagnetic stresses, with emphasis on homogeneous magnetoelectric material. An explicit calculation of the average pressure exerted by a monochromatic wave normally incident on a homogeneous, magnetoelectric slab in vacuo is presented and the concluding section summarizes how this pressure depends on the parameters in the magnetoelectric tensors for the medium.Comment: 25 pages, 3 figures, to appear in Il Nuovo Cimento B, proceedings of GCM8, Catania (Oct 2008) - References added, minor corrections mad

Solutions for Neutral for Axi-Dilaton Gravity in 4-Dimensions

We examine a 1 parameter class of actions describing the gravitational interaction between a pair of scalar fields and Einsteinian gravitation. When the parameter is positive the theory corresponds to an axi-dilatonic sector of low energy string theory. We exploit an SL(2,R) symmetry of the theory to construct a family of electromagnetically neutral solutions with non-zero axion and dilaton charge from solutions of the Brans-Dicke theory. We also comment on solutions to the theory with negative coupling parameter.Comment: 7 pages Plain Tex (No Figures), Letter to Editor, Classical and Quantum Gravit

Mobile radio alternative systems study. Volume 1: Traffic model

The markets for mobile radio services in non-urban areas of the United States are examined for the years 1985-2000. Three market categories are identified. New Services are defined as those for which there are different expressed ideas but which are not now met by any application of available technology. The complete fulfillment of the needs requires nationwide radio access to vehicles without knowledge of vehicle location, wideband data transmission from remote sites, one- and two way exchange of short data and control messages between vehicles and dispatch or control centers, and automatic vehicle location (surveillance). The commercial and public services market of interest to the study is drawn from existing users of mobile radio in non-urban areas who are dissatisfied with the geographical range or coverage of their systems. The mobile radio telephone market comprises potential users who require access to the public switched telephone network in areas that are not likely to be served by the traditional growth patterns of terrestrial mobile telephone services. Conservative, likely, and optimistic estimates of the markets are presented in terms of numbers of vehicles that will be served and the radio traffic they will generate

An architecture for integrating distributed and cooperating knowledge-based Air Force decision aids

MITRE has been developing a Knowledge-Based Battle Management Testbed for evaluating the viability of integrating independently-developed knowledge-based decision aids in the Air Force tactical domain. The primary goal for the testbed architecture is to permit a new system to be added to a testbed with little change to the system's software. Each system that connects to the testbed network declares that it can provide a number of services to other systems. When a system wants to use another system's service, it does not address the server system by name, but instead transmits a request to the testbed network asking for a particular service to be performed. A key component of the testbed architecture is a common database which uses a relational database management system (RDBMS). The RDBMS provides a database update notification service to requesting systems. Normally, each system is expected to monitor data relations of interest to it. Alternatively, a system may broadcast an announcement message to inform other systems that an event of potential interest has occurred. Current research is aimed at dealing with issues resulting from integration efforts, such as dealing with potential mismatches of each system's assumptions about the common database, decentralizing network control, and coordinating multiple agents