Tensor Type Research Articles

Parity Nonconservation and the Beta-Spectrum of RaE

A method suitable for analysing the anomalous f)-spectrum of RaE is developed. It is shown 1:hat, if the Gamow-Teller component of the fl-decay interaction is of the tensor type, it is very difficult to explain the shape of the f)-spectrum of RaE unless all of the following conditions are satisfied .simultaneously: (a) the Fermi component is of the scalar type, (b) Cs/Cs' =Cp/C-/, and (c) Cs/Cp=real. Alternatively, if the Gamow-Teller component is of the axial vector type, the conditions are: (a) the Fermi component is of the vector type, (b) Cv/C'v=C,.~./C,/, and (c) CvfC,.~.= real.

Energy spectrum of pions and polarization of muons and electrons in the Kμ3 and Ke3 decay

In this paper two aspects of the Kμ3 and Ke3 decay are discussed: the energy density of final states and the longitudinal polarization of the muons and electrons. It is assumed that the fermion pair is produced through a Fermi interaction which can be of scalar, vector or tensor type. The two-component theory of the neutrino is used. The energy spectra and polarization depend in general on three complex parameters. However, if the theory is to be invariant under time reversal, the parameters must be real. With the values of the parameters determined from the energy spectrum one can predict the polarization. This provides a good check of the two-component theory.

Parity Nonconservation and theβSpectrum of RaE

It is pointed out that, if the Gamow-Teller component of the- BETA - decay interaction is of the tensor type and if C/sub T/ = -C'/sub T/ (C rind C' are the parity conserving and nonconserving couping constants, respectively), it is very difficult to explain the shape of the BETA spectrum of RaE (Bi/sup 210) by the Fermi theory unless the following conditions are met approximately: (a) the Fermi component is of the scalar type; (b) C/sub S/ = - C'/sub S/: and (c) C/ sub S/C/sub T/= real. (L.T.W.)

Invariant Formulation of Gravitational Radiation Theory

In this paper, gravitational radiation is defined invariantly within the framework of general relativity theory. The definition is arrived at by assuming (a) that gravitational radiation is characterized by the Riemann tensor, and (b) that it is propagated with the fundamental velocity. Therefore a gravitational wave front should appear as a discontinuity in the Riemann tensor across a null 3-surface; the possible form of this discontinuity is here calculated from Lichnerowicz's continuity conditions. The concept of an observer who follows the gravitational field is defined in terms of the eigenbivectors of the Riemann tensor. It is shown that the 4-velocity of this observer is timelike for one of Petrov's three canonical types of Riemann tensor, but null for the other two types. The first type is identified with the absence of radiation, the other two with its presence. This constitutes the definition. It is shown that the difference between the no-radiation type and one of the radiation types can be made to correspond to the discontinuity possible across a null 3-surface; this demonstrates the consistency of the wave front and following-the-field concepts. A covariant approximation to the canonical energy-momentum pseudo-tensor is defined, using normal coordinates, which are given a physical interpretation. It is shown that when gravitational radiation is present, the approximate gravitational energy-flux cannot be removed by a local Lorentz transformation, which supports the definition of radiation. It is proved that, as would be demanded of a sensible definition, there can be no gravitational radiation present in a region of empty space-time where the metric is static.

Morphogenesis of the architecture of hip and thigh

AbstractThe original innominate bone consisted of ischiopubis only. From this developed a dorsally‐directed ilium, upon which the dorsal limb muscles, originally arising from fascia, settled, and which thrust dorsalward between roots of the limb plexus, thus dividing the nerves into prozonal (dorsal and ventral) and metazonal (dorsal and ventral) groups. The primitive muscles of the tetrapod hip and thigh comprised a dorsal mass, soon divisible into sheets, innervated by both prozonal and metazonal dorsal nerves, and a similar ventral mass comparably innervated. The original two elements thus became four basic elements, and probably in early mammals or mammal‐like reptiles all dually innervated muscles split into singly innervated units. With this four‐group basis as the chief criterion, but considering other factors as well, it is possible to homologize the muscles of urodeles (ventral components only), lacertilians, mammals, and birds in entirely satisfactory manner, except for doubt in several instances in which specialization has secondarily obscured the precise relationships. In different mammals there is shown a tendency toward a final fusion of certain unrelated muscle units (biceps plus gluteus longus, human type of biceps, adductor magnus, and tensor fasciae femoris with gluteus maximus).

On the classification of asymptotic quasinormal frequencies for {$d$}-dimensional black holes and quantum gravity

We provide a complete classification of asymptotic quasinormal frequencies for static, spherically symmetric black hole spacetimes in d dimensions. This includes all possible types of gravitational perturbations (tensor, vector and scalar type) as described by the Ishibashi–Kodama master equations. The frequencies for Schwarzschild are dimension independent, while for Reissner–Nordstrom are dimension dependent (the extremal Reissner–Nordstrom case must be considered separately from the non–extremal case). For Schwarzschild de Sitter, there is a dimension independent formula for the frequencies, except in dimension d = 5 where the formula is different. For Reissner–Nordstrom de Sitter there is a dimension dependent formula for the frequencies, except in dimension d = 5 where the formula is different. Schwarzschild and Reissner–Nordstrom Anti–de Sitter black hole spacetimes are simpler: the formulae for the frequencies will depend upon a parameter related to the tortoise coordinate at spatial infinity, and scalar type perturbations in dimension d = 5 lead to a continuous spectrum for the quasinormal frequencies. We also address non–black hole spacetimes, such as pure de Sitter spacetime—where there are quasinormal modes only in odd dimensions—and pure Anti–de Sitter spacetime—where again scalar type perturbations in dimension d = 5 lead to a continuous spectrum for the normal frequencies. Our results match previous numerical calculations with great accuracy. Asymptotic quasinormal frequencies have also been applied in the framework of quantum gravity for black holes. Our results show that it is only in the simple Schwarzschild case which is possible to obtain sensible results concerning area quantization or loop quantum gravity. In an effort to keep this paper self–contained we also review earlier results in the literature.