Reciprocal relativity of noninertial frames: quantum mechanics

Noninertial transformations on time-position-momentum-energy space {t,q,p,e} with invariant Born-Green metric ds^2=-dt^2+dq^2/c^2+(1/b^2)(dp^2-de^2/c^2) and the symplectic metric -de/\dt+dp/\dq are studied. This U(1,3) group of transformations contains the Lorentz group as the inertial special case. In the limit of small forces and velocities, it reduces to the expected Hamilton transformations leaving invariant the symplectic metric and the nonrelativistic line element ds^2=dt^2. The U(1,3) transformations bound relative velocities by c and relative forces by b. Spacetime is no longer an invariant subspace but is relative to noninertial observer frames. Born was lead to the metric by a concept of reciprocity between position and momentum degrees of freedom and for this reason we call this reciprocal relativity. For large b, such effects will almost certainly only manifest in a quantum regime. Wigner showed that special relativistic quantum mechanics follows from the projective representations of the inhomogeneous Lorentz group. Projective representations of a Lie group are equivalent to the unitary reprentations of its central extension. The same method of projective representations of the inhomogeneous U(1,3) group is used to define the quantum theory in the noninertial case. The central extension of the inhomogeneous U(1,3) group is the cover of the quaplectic group Q(1,3)=U(1,3)*s H(4). H(4) is the Weyl-Heisenberg group. A set of second order wave equations results from the representations of the Casimir operators

Kinematics of women's sprint canoeing technique

Little is known about the biomechanics of sprint canoeing, especially for women’s canoeing, and a quantitative kinematic description of the motion would help coaches to develop valid technique coaching models. Five highly-trained female canoeists were filmed at 150 Hz while undertaking a 50 s maximal effort on a canoe ergometer, whose trolley motions were taken to represent those of the boat. Selected boat, body and paddle kinematics were evaluated at three key stroke cycle events (Contact, Paddle Vertical, and End of Drive) and their patterns monitored across the stroke cycle. While no clear trends between the kinematics and power output emerged, a range of strategies were identified and the data represent an initial step in the construction of detailed technique models that can be used to evaluate and monitor individual athletes

2,6-Diiodo-4-nitrophenol, 2,6-diiodo-4-nitrophenyl acetate and 2,6-diiodo-4-nitroanisole: interplay of hydrogen bonds, iodo-nitro interactions and aromatic [pi]-[pi]-stacking interactions to give supramolecular structures in one, two and three dimensions

Peer reviewedPublisher PD

Density, Velocity, and Magnetic Field Structure in Turbulent Molecular Cloud Models

We use 3D numerical MHD simulations to follow the evolution of cold, turbulent, gaseous systems with parameters representing GMC conditions. We study three cloud simulations with varying mean magnetic fields, but identical initial velocity fields. We show that turbulent energy is reduced by a factor two after 0.4-0.8 flow crossing times (2-4 Myr), and that the magnetically supercritical cloud models collapse after ~6 Myr, while the subcritical cloud does not collapse. We compare density, velocity, and magnetic field structure in three sets of snapshots with matched Mach numbers. The volume and column densities are both log-normally distributed, with mean volume density a factor 3-6 times the unperturbed value, but mean column density only a factor 1.1-1.4 times the unperturbed value. We use a binning algorithm to investigate the dependence of kinetic quantities on spatial scale for regions of column density contrast (ROCs). The average velocity dispersion for the ROCs is only weakly correlated with scale, similar to the mean size-linewidth relation for clumps within GMCs. ROCs are often superpositions of spatially unconnected regions that cannot easily be separated using velocity information; the same difficulty may affect observed GMC clumps. We analyze magnetic field structure, and show that in the high density regime, total magnetic field strengths increase with density with logarithmic slope 1/3 -2/3. Mean line-of-sight magnetic field strengths vary widely across a projected cloud, and do not correlate with column density. We compute simulated interstellar polarization maps at varying orientations, and determine that the Chandrasekhar-Fermi formula multiplied by a factor ~0.5 yields a good estimate of the plane-of sky magnetic field strength provided the dispersion in polarization angles is < 25 degrees.Comment: 56 pages, 25 figures; Ap.J., accepte

Low-energy interaction of composite spin-half systems with scalar and vector fields

We consider a composite spin-half particle moving in spatially-varying scalar and vector fields. The vector field is assumed to couple to a conserved charge, but no assumption is made about either the structure of the composite or its coupling to the scalar field. A general form for the piece of the spin-orbit interaction of the composite with the scalar and vector fields which is first-order in momentum transfer ${\bf Q}$ and second-order in the fields is derived.Comment: 10 pages, RevTe

Bremsstrahlung in Alpha-Decay

We present the first fully quantum mechanical calculation of photon radiation accompanying charged particle decay from a barrier resonance. The soft-photon limit agrees with the classical results, but differences appear at next-to-leading-order. Under the conditions of alpha-decay of heavy nuclei, the main contribution to the photon emission stems from Coulomb acceleration and may be computed analytically. We find only a small contribution from the tunneling wave function under the barrier.Comment: 12 pages, 2 Postscript figure

Multiple Reggeon Exchange from Summing QCD Feynman Diagrams

Multiple reggeon exchange supplies subleading logs that may be used to restore unitarity to the Low-Nussinov Pomeron, provided it can be proven that the sum of Feynman diagrams to all orders gives rise to such multiple regge exchanges. This question cannot be easily tackled in the usual way except for very low-order diagrams, on account of delicate cancellations present in the sum which necessitate individual Feynman diagrams to be computed to subleading orders. Moreover, it is not clear that sums of high-order Feynman diagrams with complicated criss-crossing of lines can lead to factorization implied by the multi-regge scenario. Both of these difficulties can be overcome by using the recently developed nonabelian cut diagrams. We are then able to show that the sum of $s$-channel-ladder diagrams to all orders does lead to such multiple reggeon exchanges.Comment: uu-encoded latex file with 11 postscript figures (20 pages

Color mixing in high-energy hadron collisions

The color mixing of mesons propagating in a nucleus is studied with the help of a color-octet Pomeron partner present in the two-gluon model of the Pomeron. For a simple model with four meson-nucleon channels, color mixings are found to be absent for pointlike mesons and very small for small mesons. These results seem to validate the absorption model with two independent color components used in recent analyses of the nuclear absorption of $J/\psi$ mesons produced in nuclear reactions.Comment: 3 journal-style page

MIPS: The Multiband Imaging Photometer for SIRTF

The Multiband Imaging Photometer for SIRTF (MIPS) is to be designed to reach as closely as possible the fundamental sensitivity and angular resolution limits for SIRTF over the 3 to 700μm spectral region. It will use high performance photoconductive detectors from 3 to 200μm with integrating JFET amplifiers. From 200 to 700μm, the MIPS will use a bolometer cooled by an adiabatic demagnetization refrigerator. Over much of its operating range, the MIPS will make possible observations at and beyond the conventional Rayleigh diffraction limit of angular resolution

Bound States and Threshold Resonances in Quantum Wires with Circular Bends

We study the solutions to the wave equation in a two-dimensional tube of unit width comprised of two straight regions connected by a region of constant curvature. We introduce a numerical method which permits high accuracy at high curvature. We determine the bound state energies as well as the transmission and reflection matrices, ${\cal T}$ and ${\cal R}$ and focus on the nature of the resonances which occur in the vicinity of channel thresholds. We explore the dependence of these solutions on the curvature of the tube and angle of the bend and discuss several limiting cases where our numerical results confirm analytic predictions.Comment: 24 pages, revtex file, one style file and 17 PostScript figures include