A geometric basis for the standard-model gauge group

A geometric approach to the standard model in terms of the Clifford algebra Cl_7 is advanced. A key feature of the model is its use of an algebraic spinor for one generation of leptons and quarks. Spinor transformations separate into left-sided ("exterior") and right-sided ("interior") types. By definition, Poincare transformations are exterior ones. We consider all rotations in the seven-dimensional space that (1) conserve the spacetime components of the particle and antiparticle currents and (2) do not couple the right-chiral neutrino. These rotations comprise additional exterior transformations that commute with the Poincare group and form the group SU(2)_L, interior ones that constitute SU(3)_C, and a unique group of coupled double-sided rotations with U(1)_Y symmetry. The spinor mediates a physical coupling of Poincare and isotopic symmetries within the restrictions of the Coleman--Mandula theorem. The four extra spacelike dimensions in the model form a basis for the Higgs isodoublet field, whose symmetry requires the chirality of SU(2). The charge assignments of both the fundamental fermions and the Higgs boson are produced exactly.Comment: 17 pages, LaTeX requires iopart. Accepted for publication in J. Phys. A: Math. Gen. 9 Mar 2001. Typos correcte

Development and flight test of a helicopter compact, portable, precision landing system concept

An airborne, radar-based, precision approach concept is being developed and flight tested as a part of NASA's Rotorcraft All-Weather Operations Research Program. A transponder-based beacon landing system (BLS) applying state-of-the-art X-band radar technology and digital processing techniques, was built and is being flight tested to demonstrate the concept feasibility. The BLS airborne hardware consists of an add-on microprocessor, installed in conjunction with the aircraft weather/mapping radar, which analyzes the radar beacon receiver returns and determines range, localizer deviation, and glide-slope deviation. The ground station is an inexpensive, portable unit which can be quickly deployed at a landing site. Results from the flight test program show that the BLS concept has a significant potential for providing rotorcraft with low-cost, precision instrument approach capability in remote areas

Development and flight test of a helicopter, X-band, portable precision landing system concept

A beacon landing system (BLS) is being developed and flight tested as a part of NASA's Rotorcraft All-Weather Operations Research Program. The system is based on state-of-of-the-art X-band radar technology and digital processing techniques. The bLS airborne hardware consists of an X-band receiver and a small micropreocessor, installed in conjunction wht the aircraft instrument landing system (ILS) receiver. The microprocessor analyzes the X-band, BLS pulses and outputs ILS-compatible localizer and glide slope signals. Range information is obtained using an on-board weather/mapping radar in conjunction with the BLS. The ground station is an inexpensive, portable unit; it weighs less than 70 lb and can be quickly deployed at a landing site. Results from the flight-test program show that the BLS has a significant potential for providing rotorcaraft with low-cost, precision instrument approach capability in remote areas

The Off-Shell Nucleon-Nucleon Amplitude: Why it is Unmeasurable in Nucleon-Nucleon Bremsstrahlung

Nucleon-nucleon bremsstrahlung has long been considered a way of getting information about the off-shell nucleon-nucleon amplitude which would allow one to distinguish among nucleon-nucleon potentials based on their off-shell properties. There have been many calculations and many experiments devoted to this aim. We show here, in contrast to this standard view, that such off-shell amplitudes are not measurable as a matter of principle. This follows formally from the invariance of the S-matrix under transformations of the fields. This result is discussed here and illustrated via two simple models, one applying to spin zero, and one to spin one half, processes. The latter model is very closely related to phenomenological models which have been used to study off-shell effects at electromagnetic vertices.Comment: 6 pages, Latex, uses FBSsuppl.cls - Invited plenary talk at the Asia Pacific Conference on Few Body Problems in Physics, Noda/Kashiwa, Japan, August, 1999 - To be published in Few Body Systems Supp

Accurately predicting the escape fraction of ionizing photons using restframe ultraviolet absorption lines

The fraction of ionizing photons that escape high-redshift galaxies sensitively determines whether galaxies reionized the early universe. However, this escape fraction cannot be measured from high-redshift galaxies because the opacity of the intergalactic medium is large at high redshifts. Without methods to indirectly measure the escape fraction of high-redshift galaxies, it is unlikely that we will know what reionized the universe. Here, we analyze the far-ultraviolet (UV) H I (Lyman series) and low-ionization metal absorption lines of nine low-redshift, confirmed Lyman continuum emitting galaxies. We use the H I covering fractions, column densities, and dust attenuations measured in a companion paper to predict the escape fraction of ionizing photons. We find good agreement between the predicted and observed Lyman continuum escape fractions (within $1.4\sigma$) using both the H I and ISM absorption lines. The ionizing photons escape through holes in the H I, but we show that dust attenuation reduces the fraction of photons that escape galaxies. This means that the average high-redshift galaxy likely emits more ionizing photons than low-redshift galaxies. Two other indirect methods accurately predict the escape fractions: the Ly$\alpha$ escape fraction and the optical [O III]/[O II] flux ratio. We use these indirect methods to predict the escape fraction of a sample of 21 galaxies with rest-frame UV spectra but without Lyman continuum observations. Many of these galaxies have low escape fractions ($f_{\rm esc} \le 1$\%), but 11 have escape fractions $>1$\%. The methods presented here will measure the escape fractions of high-redshift galaxies, enabling future telescopes to determine whether star-forming galaxies reionized the early universe.Comment: Accepted for publication in A&A. 12 pages, 5 figure

Interaction control and bright solitons in coherently-coupled Bose-Einstein condensates

We demonstrate fast control of the interatomic interactions in a Bose-Einstein condensate by coherently coupling two atomic states with intra- and inter-state scattering lengths of opposite signs. We measure the elastic and inelastic scattering properties of the system and find good agreement with a theoretical model describing the interactions between dressed states. In the attractive regime, we observe the formation of bright solitons formed by dressed-state atoms. Finally, we study the response of the system to an interaction quench from repulsive to attractive values, and observe how the resulting modulational instability develops into a bright soliton train.Comment: 6 pages, 4 figure

Stellar-Mass Black Holes in the Solar Neighborhood

We search for nearby, isolated, accreting, ``stellar-mass'' (3 to $100M_\odot$) black holes. Models suggest a synchrotron spectrum in visible wavelengths and some emission in X-ray wavelengths. Of 3.7 million objects in the Sloan Digital Sky Survey Early Data Release, about 150,000 objects have colors and properties consistent with such a spectrum, and 87 of these objects are X-ray sources from the ROSAT All Sky Survey. Thirty-two of these have been confirmed not to be black-holes using optical spectra. We give the positions and colors of these 55 black-hole candidates, and quantitatively rank them on their likelihood to be black holes. We discuss uncertainties the expected number of sources, and the contribution of blackholes to local dark matter.Comment: Replaced with version accepted by ApJ. 40 pages, 8 figure

The exponential map for the unitary group SU(2,2)

In this article we extend our previous results for the orthogonal group, $SO(2,4)$, to its homomorphic group $SU(2,2)$. Here we present a closed, finite formula for the exponential of a $4\times 4$ traceless matrix, which can be viewed as the generator (Lie algebra elements) of the $SL(4,C)$ group. We apply this result to the $SU(2,2)$ group, which Lie algebra can be represented by the Dirac matrices, and discuss how the exponential map for $SU(2,2)$ can be written by means of the Dirac matrices.Comment: 10 page

Kelvin mode of a vortex in a nonuniform Bose-Einstein condensate

In a uniform fluid, a quantized vortex line with circulation h/M can support long-wavelength helical traveling waves proportional to e^{i(kz-\omega_k t)} with the well-known Kelvin dispersion relation \omega_k \approx (\hbar k^2/2M) \ln(1/|k|\xi), where \xi is the vortex-core radius. This result is extended to include the effect of a nonuniform harmonic trap potential, using a quantum generalization of the Biot-Savart law that determines the local velocity V of each element of the vortex line. The normal-mode eigenfunctions form an orthogonal Sturm-Liouville set. Although the line's curvature dominates the dynamics, the transverse and axial trapping potential also affect the normal modes of a straight vortex on the symmetry axis of an axisymmetric Thomas-Fermi condensate. The leading effect of the nonuniform condensate density is to increase the amplitude along the axis away from the trap center. Near the ends, however, a boundary layer forms to satisfy the natural Sturm-Liouville boundary conditions. For a given applied frequency, the next-order correction renormalizes the local wavenumber k(z) upward near the trap center, and k(z) then increases still more toward the ends.Comment: 9 pages, 1 figur

In-medium meson properties and field transformations

Since the existing calculations of the effective meson mass in nuclear medium involve approximations, it is important to examine whether they satisfy the general requirement of the equivalence theorem that the physical observables should be independent of the choice of field variables. We study here consequences of nucleon field transformations. As an illustrative case we consider the in-medium effective pion mass calculated for the s-wave pion-nucleon interaction in the linear density approximation. We demonstrate that it is necessary to include the Born term explicitly in order that the effective pion mass should obey the equivalence theorem.Comment: 10 pages, using RevTeX4. More detailed discussion, references added. To be published in Phys. Rev.