Putting an Edge to the Poisson Bracket

We consider a general formalism for treating a Hamiltonian (canonical) field theory with a spatial boundary. In this formalism essentially all functionals are differentiable from the very beginning and hence no improvement terms are needed. We introduce a new Poisson bracket which differs from the usual ``bulk'' Poisson bracket with a boundary term and show that the Jacobi identity is satisfied. The result is geometrized on an abstract world volume manifold. The method is suitable for studying systems with a spatial edge like the ones often considered in Chern-Simons theory and General Relativity. Finally, we discuss how the boundary terms may be related to the time ordering when quantizing.Comment: 36 pages, LaTeX. v2: A manifest formulation of the Poisson bracket and some examples are added, corrected a claim in Appendix C, added an Appendix F and a reference. v3: Some comments and references adde

Statistical evaluation of control inputs and eye movements in the use of instruments clusters during aircraft landing

Two different types of analyses were done on data from a study in which eye movements and other variables were recorded while four pilots executed landing sequences in a Boeing 737 simulation. Various conditions were manupulated, including changes in turbulence, starting position, and instrumentation. Control inputs were analyzed in the context of the various conditions and compared against ratings of workload obtained using the Cooper-Harper scale. A number of eye-scanning measures including mean dwell time and transition from one instrument to another were entered into a principal components factor analysis. The results show a differentiation between control inputs and eye-scanning behavior. This shows the need for improved definition of workload and experiments to uncover the important differences among control inputs, eye-scanning and cognitive processes of the pilot

Time-Reversal-Violating Schiff Moment of 199Hg

We calculate the Schiff moment of the nucleus 199Hg, created by pi-N-N vertices that are odd under parity (P) and time-reversal (T). Our approach, formulated in diagrammatic perturbation theory with important core-polarization diagrams summed to all orders, gives a close approximation to the expectation value of the Schiff operator in the odd-A Hartree-Fock-Bogoliubov ground state generated by a Skyrme interaction and a weak P- and T-odd pion-exchange potential. To assess the uncertainty in the results, we carry out the calculation with several Skyrme interactions (the quality of which we test by checking predictions for the isoscalar-E1 strength distribution in 208Pb) and estimate most of the important diagrams we omit.Comment: 13 pages, 7 figure

Sums and differences of four k-th powers

We prove an upper bound for the number of representations of a positive integer $N$ as the sum of four $k$-th powers of integers of size at most $B$, using a new version of the Determinant method developed by Heath-Brown, along with recent results by Salberger on the density of integral points on affine surfaces. More generally we consider representations by any integral diagonal form. The upper bound has the form $O_{N}(B^{c/\sqrt{k}})$, whereas earlier versions of the Determinant method would produce an exponent for $B$ of order $k^{-1/3}$ in this case. Furthermore, we prove that the number of representations of a positive integer $N$ as a sum of four $k$-th powers of non-negative integers is at most $O_{\epsilon}(N^{1/k+2/k^{3/2}+\epsilon})$ for $k \geq 3$, improving upon bounds by Wisdom.Comment: 18 pages. Mistake corrected in the statement of Theorem 1.2. To appear in Monatsh. Mat

Recent developments in perturbation theory

Rayleigh-Schroeder perturbation theory - degenerate and non-degenerate states - quantum chemistry - other perturbation equation

The postulates of gravitational thermodynamics

The general principles and logical structure of a thermodynamic formalism that incorporates strongly self-gravitating systems are presented. This framework generalizes and simplifies the formulation of thermodynamics developed by Callen. The definition of extensive variables, the homogeneity properties of intensive parameters, and the fundamental problem of gravitational thermodynamics are discussed in detail. In particular, extensive parameters include quasilocal quantities and are naturally incorporated into a set of basic general postulates for thermodynamics. These include additivity of entropies (Massieu functions) and the generalized second law. Fundamental equations are no longer homogeneous first-order functions of their extensive variables. It is shown that the postulates lead to a formal resolution of the fundamental problem despite non-additivity of extensive parameters and thermodynamic potentials. Therefore, all the results of (gravitational) thermodynamics are an outgrowth of these postulates. The origin and nature of the differences with ordinary thermodynamics are analyzed. Consequences of the formalism include the (spatially) inhomogeneous character of thermodynamic equilibrium states, a reformulation of the Euler equation, and the absence of a Gibbs-Duhem relation.Comment: 28 pages, Revtex, no figures. An important sentence and several minor corrections included. To appear in Physical Review

Competing With the NYSE

We study the stock exchange rivalry between the New York Stock Exchange (NYSE) and the Consolidated Stock Exchange (Consolidated) from 1885 to 1926 using a new database of bid-ask spreads and stock data collected from The New York Times and other primary sources. The magnitude of this important, but largely forgotten rivalry was substantial. From 1885 to 1895, the ratio of Consolidated to NYSE volume averaged 40 percent and reached as high as 60 percent. The market share of the Consolidated averaged 23 percent for approximately 40 years. The Consolidated focused on the relatively liquid securities on the NYSE as measured by bid-ask spreads and trading volume. Our results suggest that NYSE bid-ask spreads fell by more than 10 percent when the Consolidated began to trade NYSE stocks while bid-ask spreads for our quasicontrol group of stocks trading on the Boston Stock Exchange remain unchanged. The effect persisted over the entire history of the stock market rivalry until a series of scandals and investigations of the Consolidated by state regulators led to the demise of the exchange in the 1920s. The analysis suggests three conclusions: (1) the NYSE has faced significant long-run competition (2) the NYSE may be susceptible to a similar level of competition in the future and (3) that the Consolidated may have improved the efficiency of stock prices by contributing to the price discovery process.