Quasilocal Conservation Laws: Why We Need Them

We argue that conservation laws based on the local matter-only stress-energy-momentum tensor (characterized by energy and momentum per unit volume) cannot adequately explain a wide variety of even very simple physical phenomena because they fail to properly account for gravitational effects. We construct a general quasi}local conservation law based on the Brown and York total (matter plus gravity) stress-energy-momentum tensor (characterized by energy and momentum per unit area), and argue that it does properly account for gravitational effects. As a simple example of the explanatory power of this quasilocal approach, consider that, when we accelerate toward a freely-floating massive object, the kinetic energy of that object increases (relative to our frame). But how, exactly, does the object acquire this increasing kinetic energy? Using the energy form of our quasilocal conservation law, we can see precisely the actual mechanism by which the kinetic energy increases: It is due to a bona fide gravitational energy flux that is exactly analogous to the electromagnetic Poynting flux, and involves the general relativistic effect of frame dragging caused by the object's motion relative to us.Comment: 20 pages, 1 figur

Dirac versus Reduced Quantization of the Poincar\'{e} Symmetry in Scalar Electrodynamics

The generators of the Poincar\'{e} symmetry of scalar electrodynamics are quantized in the functional Schr\"{o}dinger representation. We show that the factor ordering which corresponds to (minimal) Dirac quantization preserves the Poincar\'{e} algebra, but (minimal) reduced quantization does not. In the latter, there is a van Hove anomaly in the boost-boost commutator, which we evaluate explicitly to lowest order in a heat kernel expansion using zeta function regularization. We illuminate the crucial role played by the gauge orbit volume element in the analysis. Our results demonstrate that preservation of extra symmetries at the quantum level is sometimes a useful criterion to select between inequivalent, but nevertheless self-consistent, quantization schemes.Comment: 24 page

Rectenna for high-voltage applications

An energy transfer system is disclosed. The system includes patch elements, shielding layers, and energy rectifying circuits. The patch elements receive and couple radio frequency energy. The shielding layer includes at least one opening that allows radio frequency energy to pass through. The openings are formed and positioned to receive the radio frequency energy and to minimize any re-radiating back toward the source of energy. The energy rectifying circuit includes a circuit for rectifying the radio frequency energy into dc energy. A plurality of energy rectifying circuits is arranged in an array to provide a sum of dc energy generated by the energy rectifying circuit

Electoral turnover has very little effect on the spending habits of Western democracies

Do new electoral brooms sweep clean the economic policies of the parties that went before? In new research that examines how incoming Western governments set their spending priorities, Derek A. Epp, John Lovett, and Frank R. Baumgartner find that budgets tend to be set with little regard to a government’s ideology, be it left or right. They argue that when setting budgets, incoming policymakers are constrained by social, economic and international realities that are largely beyond their control. This means that budgets are set consistently and inconsistently with what went before at roughly the same rate; left-wing parties do not necessarily favor “big government” nor to right parties always seek to reduce government spending

Wideband radial power combiner/divider fed by a mode transducer

A radial power combiner/divider capable of a higher order (for example, N=24) of power combining/dividing and a 15% bandwidth (31 to 36 GHz). The radial power combiner/divider generally comprises an axially-oriented mode transducer coupled to a radial base. The mode transducer transduces circular TE01 waveguide into rectangular TE10 waveguide, and the unique radial base combines/divides a plurality of peripheral rectangular waveguide ports into a single circular TE01 waveguide end of the transducer. The radial base incorporates full-height waveguides that are stepped down to reduced-height waveguides to form a stepped-impedance configuration, thereby reducing the height of the waveguides inside the base and increasing the order N of combining/dividing. The reduced-height waveguides in the base converge radially to a matching post at the bottom center of the radial base which matches the reduced height rectangular waveguides into the circular waveguide that feeds the mode transducer

Properties of the symplectic structure of General Relativity for spatially bounded spacetime regions

We continue a previous analysis of the covariant Hamiltonian symplectic structure of General Relativity for spatially bounded regions of spacetime. To allow for near complete generality, the Hamiltonian is formulated using any fixed hypersurface, with a boundary given by a closed spacelike 2-surface. A main result is that we obtain Hamiltonians associated to Dirichlet and Neumann boundary conditions on the gravitational field coupled to matter sources, in particular a Klein-Gordon field, an electromagnetic field, and a set of Yang-Mills-Higgs fields. The Hamiltonians are given by a covariant form of the Arnowitt-Deser-Misner Hamiltonian modified by a surface integral term that depends on the particular boundary conditions. The general form of this surface integral involves an underlying ``energy-momentum'' vector in the spacetime tangent space at the spatial boundary 2-surface. We give examples of the resulting Dirichlet and Neumann vectors for topologically spherical 2-surfaces in Minkowski spacetime, spherically symmetric spacetimes, and stationary axisymmetric spacetimes. Moreover, we show the relation between these vectors and the ADM energy-momentum vector for a 2-surface taken in a limit to be spatial infinity in asymptotically flat spacetimes. We also discuss the geometrical properties of the Dirichlet and Neumann vectors and obtain several striking results relating these vectors to the mean curvature and normal curvature connection of the 2-surface. Most significantly, the part of the Dirichlet vector normal to the 2-surface depends only the spacetime metric at this surface and thereby defines a geometrical normal vector field on the 2-surface. Properties and examples of this normal vector are discussed.Comment: 46 pages; minor errata corrected in Eqs. (3.15), (3.24), (4.37) and in discussion of examples in sections IV B,