Massless Scalar Field Propagator in a Quantized Space-Time

We consider in detail the analytic behaviour of the non-interacting massless scalar field two-point function in H.S. Snyder's discretized non-commuting spacetime. The propagator we find is purely real on the Euclidean side of the complex $p^2$ plane and goes like $1/p^2$ as $p^2\to 0$ from either the Euclidean or Minkowski side. The real part of the propagator goes smoothly to zero as $p^2$ increases to the discretization scale $1/a^2$ and remains zero for $p^2>1/a^2$. This behaviour is consistent with the termination of single-particle propagation on the ultraviolet side of the discretization scale. The imaginary part of the propagator, consistent with a multiparticle-production branch discontinuity, is finite and continuous on the Minkowski side, slowly falling to zero when $1/a^2<p^2<\infty$. Finally, we argue that the spectral function for the multiparticle states appears to saturate as $p^2$ probes just beyond the $1/a^2$ discretization scale. We speculate on the cosmological consequences of such a spectral function.Comment: 6 pages, 1 eps figure embedded in manuscrip

Detection of high k turbulence using two dimensional phase contrast imaging on LHD

High k turbulence, up to 30 cm(-1), can be measured using the two dimensional CO₂ laser phase contrast imaging system on LHD. Recent hardware improvements and experimental results are presented. Precise control over the lens positions in the detection system is necessary because of the short depth of focus for high k modes. Remote controllable motors to move optical elements were installed, which, combined with measurements of the response to ultrasound injection, allowed experimental verification and shot-to-shot adjustment of the object plane. Strong high k signals are observed within the first 100-200 ms after the initial electron cyclotron heating (ECH) breakdown, in agreement with gyrotron scattering. During later times in the discharge, the entire k spectrum shifts to lower values (although the total amplitude does not change significantly), and the weaker high k signals are obscured by leakage of low k components at low frequency, and detector noise, at high frequency

Nucleosynthesis in Core-Collapse Supernovae and GRB--Metal-Poor Star Connection

We review the nucleosynthesis yields of core-collapse supernovae (SNe) for various stellar masses, explosion energies, and metallicities. Comparison with the abundance patterns of metal-poor stars provides excellent opportunities to test the explosion models and their nucleosynthesis. We show that the abundance patterns of extremely metal-poor (EMP) stars, e.g., the excess of C, Co, Zn relative to Fe, are in better agreement with the yields of hyper-energetic explosions (Hypernovae, HNe) rather than normal supernovae. We note that the variation of the abundance patterns of EMP stars are related to the diversity of the Supernova-GRB connection. We summarize the diverse properties of (1) GRB-SNe, (2) Non-GRB HNe/SNe, (3) XRF-SN, and (4) Non-SN GRB. In particular, the Non-SN GRBs (dark hypernovae) have been predicted in order to explain the origin of C-rich EMP stars. We show that these variations and the connection can be modeled in a unified manner with the explosions induced by relativistic jets. Finally, we examine whether the most luminous supernova 2006gy can be consistently explained with the pair-instability supernova model.Comment: 15 pages, 9 figures. To appear in "Supernova 1987A: 20 Years After: Supernovae and Gamma-Ray Bursters", eds. S. Immler, K. Weiler, & R. McCray (American Institute of Physics) (2007

The adiabatic evolution of orbital parameters in the Kerr spacetime

We investigate the adiabatic orbital evolution of a point particle in the Kerr spacetime due to the emission of gravitational waves. In the case that the timescale of the orbital evolution is enough smaller than the typical timescale of orbits, the evolution of orbits is characterized by the change rates of three constants of motion, the energy $E$, the azimuthal angular momentum $L$, and the Carter constant $Q$. For $E$ and $L$, we can evaluate their change rates from the fluxes of the energy and the angular momentum at infinity and on the event horizon according to the balance argument. On the other hand, for the Carter constant, we cannot use the balance argument because we do not know the conserved current associated with it. %and the corresponding conservation law. Recently, Mino proposed a new method of evaluating the averaged change rate of the Carter constant by using the radiative field. In our previous paper we developed a simplified scheme for practical evaluation of the evolution of the Carter constant based on the Mino's proposal. In this paper we describe our scheme in more detail, and derive explicit analytic formulae for the change rates of the energy, the angular momentum and the Carter constant.Comment: 34 pages, no figur

Non-Universal Critical Behaviour of Two-Dimensional Ising Systems

Two conditions are derived for Ising models to show non-universal critical behaviour, namely conditions concerning 1) logarithmic singularity of the specific heat and 2) degeneracy of the ground state. These conditions are satisfied with the eight-vertex model, the Ashkin-Teller model, some Ising models with short- or long-range interactions and even Ising systems without the translational or the rotational invariance.Comment: 17 page

The Connection between Gamma-Ray Bursts and Extremely Metal-Poor Stars as Nucleosynthetic Probes of the Early Universe

The connection between the long GRBs and Type Ic Supernovae (SNe) has revealed the interesting diversity: (i) GRB-SNe, (ii) Non-GRB Hypernovae (HNe), (iii) X-Ray Flash (XRF)-SNe, and (iv) Non-SN GRBs (or dark HNe). We show that nucleosynthetic properties found in the above diversity are connected to the variation of the abundance patterns of extremely-metal-poor (EMP) stars, such as the excess of C, Co, Zn relative to Fe. We explain such a connection in a unified manner as nucleosynthesis of hyper-aspherical (jet-induced) explosions Pop III core-collapse SNe. We show that (1) the explosions with large energy deposition rate, $\dot{E}_{\rm dep}$, are observed as GRB-HNe and their yields can explain the abundances of normal EMP stars, and (2) the explosions with small $\dot{E}_{\rm dep}$ are observed as GRBs without bright SNe and can be responsible for the formation of the C-rich EMP (CEMP) and the hyper metal-poor (HMP) stars. We thus propose that GRB-HNe and the Non-SN GRBs (dark HNe) belong to a continuous series of BH-forming stellar deaths with the relativistic jets of different $\dot{E}_{\rm dep}$.Comment: 8 pages, 6 figures. To appear in "Massive Stars as Cosmic Engines", Proceedings of IAU Symposium 250 (December 2007, Kauai), eds. F. Bresolin, P.A. Crowther, & J. Puls (Cambridge Univ. Press

The Unique Type Ib Supernova 2005bf at Nebular Phases: A Possible Birth Event of A Strongly Magnetized Neutron Star

Late phase nebular spectra and photometry of Type Ib Supernova (SN) 2005bf taken by the Subaru telescope at ~ 270 and ~ 310 days since the explosion are presented. Emission lines ([OI]6300, 6363, [CaII]7291, 7324, [FeII]7155) show the blueshift of ~ 1,500 - 2,000 km s-1. The [OI] doublet shows a doubly-peaked profile. The line luminosities can be interpreted as coming from a blob or jet containing only ~ 0.1 - 0.4 Msun, in which ~ 0.02 - 0.06 Msun is 56Ni synthesized at the explosion. To explain the blueshift, the blob should either be of unipolar moving at the center-of-mass velocity v ~ 2,000 - 5,000 km s-1, or suffer from self-absorption within the ejecta as seen in SN 1990I. In both interpretations, the low-mass blob component dominates the optical output both at the first peak (~ 20 days) and at the late phase (~ 300 days). The low luminosity at the late phase (the absolute R magnitude M_R ~ -10.2 mag at ~ 270 days) sets the upper limit for the mass of 56Ni < ~ 0.08 Msun, which is in contradiction to the value necessary to explain the second, main peak luminosity (M_R ~ -18.3 mag at ~ 40 days). Encountered by this difficulty in the 56Ni heating model, we suggest an alternative scenario in which the heating source is a newly born, strongly magnetized neutron star (a magnetar) with the surface magnetic field Bmag ~ 10^{14-15} gauss and the initial spin period P0 ~ 10 ms. Then, SN 2005bf could be a link between normal SNe Ib/c and an X-Ray Flash associated SN 2006aj, connected in terms of Bmag and/or P0.Comment: 16 pages, 12 figures. Accepted by the Astrophysical Journa