Group quantization of parametrized systems II. Pasting Hilbert spaces

The method of group quantization described in the preceeding paper I is extended so that it becomes applicable to some parametrized systems that do not admit a global transversal surface. A simple completely solvable toy system is studied that admits a pair of maximal transversal surfaces intersecting all orbits. The corresponding two quantum mechanics are constructed. The similarity of the canonical group actions in the classical phase spaces on the one hand and in the quantum Hilbert spaces on the other hand suggests how the two Hilbert spaces are to be pasted together. The resulting quantum theory is checked to be equivalent to that constructed directly by means of Dirac's operator constraint method. The complete system of partial Hamiltonians for any of the two transversal surfaces is chosen and the quantum Schr\"{o}dinger or Heisenberg pictures of time evolution are constructed.Comment: 35 pages, latex, no figure

Do static sources respond to massive scalar particles from the Hawking radiation as uniformly accelerated ones do in the inertial vacuum?

We revisit the recently found equivalence for the response of a static scalar source interacting with a {\em massless} Klein-Gordon field when the source is (i) static in Schwarzschild spacetime, in the Unruh vacuum associated with the Hawking radiation and (ii) uniformly accelerated in Minkowski spacetime, in the inertial vacuum, provided that the source's proper acceleration is the same in both cases. It is shown that this equivalence is broken when the massless Klein-Gordon field is replaced by a {\em massive} one.Comment: 4 pages, 2 figure

Satellite tracking in avian conservation: applications and results from Asia

Using satellite tracking, we have followed the movements of large wetland birds in Asia for more than 10 years. We have investigated the migration patterns of more than 10 species of birds, focusing on, but not limited to, cranes (Gruidae) and storks (Ciconiidae). To relay bird locations, we employed platform transmitter terminals in combination with ARGOS satellites. Location data were then utilized in a variety of applications, from determining migration routes, stopover patterns and wintering sites, through more advanced analyses including using various data overlays to examine habitat use, occupation of nature reserves, differential migration patterns between adults and juvenile birds, climatological effects on migration and the connectivity and network structure of migration pathways. Through this work, we have identified numerous important sites for migratory birds, especially cranes and storks. These include Bohai Bay and the Yellow River delta (China), the Korean Demilitarized Zone, Lake Khanka (Russia/China), and Poyang Lake, the Qiqihar Baicheng area, the Three Rivers Plain and Yangcheng Nature Reserve (all in China). We have also developed recommendations for spatial improvements to nature reserves, discovered different migration strategies in juvenile and adult birds, and a possible migration trigger involving temperature. We emphasize the importance of continued empirical research and development of analytical methodologies involving satellite location data. Further, we advocate the protection of habitats used by Gruidae and Ciconiidae over their entire migration routes

Optical control of magnetization of micron-size domains in antiferromagnetic NiO single crystals

We propose Raman-induced collinear difference-frequency generation (DFG) as a method to manipulate dynamical magnetization. When a fundamental beam propagates along a threefold rotational axis, this coherent second-order optical process is permitted by angular momentum conservation through the rotational analogue of the Umklapp process. As a demonstration, we experimentally obtained polarization properties of collinear magnetic DFG along a [111] axis of a single crystal of antiferromagnetic NiO with micro multidomain structure, which excellently agreed with the theoretical prediction.Comment: 11 pages, 3 figures, submitted to Physical Review Letter

Interaction of Hawking radiation with static sources in deSitter and Schwarzschild-deSitter spacetimes

We study and look for similarities between the response rates $R^{\rm dS}(a_0, \Lambda)$ and $R^{\rm SdS}(a_0, \Lambda, M)$ of a static scalar source with constant proper acceleration $a_0$ interacting with a massless, conformally coupled Klein-Gordon field in (i) deSitter spacetime, in the Euclidean vacuum, which describes a thermal flux of radiation emanating from the deSitter cosmological horizon, and in (ii) Schwarzschild-deSitter spacetime, in the Gibbons-Hawking vacuum, which describes thermal fluxes of radiation emanating from both the hole and the cosmological horizons, respectively, where $\Lambda$ is the cosmological constant and $M$ is the black hole mass. After performing the field quantization in each of the above spacetimes, we obtain the response rates at the tree level in terms of an infinite sum of zero-energy field modes possessing all possible angular momentum quantum numbers. In the case of deSitter spacetime, this formula is worked out and a closed, analytical form is obtained. In the case of Schwarzschild-deSitter spacetime such a closed formula could not be obtained, and a numerical analysis is performed. We conclude, in particular, that $R^{\rm dS}(a_0, \Lambda)$ and $R^{\rm SdS}(a_0, \Lambda, M)$ do not coincide in general, but tend to each other when $\Lambda \to 0$ or $a_0 \to \infty$. Our results are also contrasted and shown to agree (in the proper limits) with related ones in the literature.Comment: ReVTeX4 file, 9 pages, 5 figure

Interaction of Hawking radiation with static sources outside a Schwarzschild black hole

We show that the response rate of (i) a static source interacting with Hawking radiation of massless scalar field in Schwarzschild spacetime (with the Unruh vacuum) and that of (ii) a uniformly accelerated source with the same proper acceleration in Minkowski spacetime (with the Minkowski vacuum) are equal. We show that this equality will not hold if the Unruh vacuum is replaced by the Hartle-Hawking vacuum. It is verified that the source responds to the Hawking radiation near the horizon as if it were at rest in a thermal bath in Minkowski spacetime with the same temperature. It is also verified that the response rate in the Hartle-Hawking vacuum approaches that in Minkowski spacetime with the same temperature far away from the black hole. Finally, we compare our results with others in the literature.Comment: 18 pages (REVTEX

Radiation from a moving Scalar Source

We study classical radiation and quantum bremsstrahlung effect of a moving point scalar source. Our classical analysis provides another example of resolving a well-known apparent paradox, that of whether a constantly accelerating source radiates or not. Quantum mechanically, we show that for a scalar source with arbitrary motion, the tree level emission rate of scalar particles in the inertial frame equals the sum of emission and absorption rates of zero-energy Rindler particles in the Rindler frame. We then explicitly verify this result for a source undergoing constant proper acceleration.Comment: 15 pages, CU-TP-59

Tree-level Scattering Amplitude in de Sitter Space

In previous papers [1,2], it was proved that a covariant quantization of the minimally coupled scalar field in de Sitter space is achieved through addition of the negative norm states. This causal approach which eliminates the infrared divergence, was generalized further to the calculation of the graviton propagator in de Sitter space [3] and one-loop effective action for scalar field in a general curved space-time [4]. This method gives a natural renormalization of the above problems. Pursuing this approach, in the present paper the tree-level scattering amplitudes of the scalar field, with one graviton exchange, has been calculated in de Sitter space. It is shown that the infrared divergence disappears and the theory automatically reaches a renormalized solution of the problem.Comment: 6 page