Universally coupled massive gravity,III: dRGT–Maheshwari pure spin-2, Ogievetsky–Polubarinov and arbitrary mass terms

Einstein’s equations were derived for a free massless spin-2 field using universal coupling in the 1950–1970s by various authors; total stress–energy including gravity’s served as a source for linear free field equations. A massive variant was likewise derived in the late 1960s by Freund, Maheshwari and Schonberg, and thought to be unique. How broad is universal coupling? In the last decade four 1-parameter families of massive spin-2 theories (contravariant, covariant, tetrad, and cotetrad of almost any density weights) have been derived using universal coupling. The (co)tetrad derivations included 2 of the 3 pure spin-2 theories due to de Rham, Gabadadze, and Tolley; those two theories first appeared in the 2-parameter Ogievetsky–Polubarinov family (1965), which developed the symmetric square root of the metric as a nonlinear group realization. One of the two theories was identified as pure spin-2 by Maheshwari in 1971–1972, thus evading the Boulware–Deser–Tyutin–Fradkin ghost by the time it was announced. Unlike the previous 4 families, this paper permits nonlinear field redefinitions to build the effective metric. By not insisting in advance on knowing the observable significance of the graviton potential to all orders, one finds that an arbitrary graviton mass term can be derived using universal coupling. The arbitrariness of a universally coupled mass/self-interaction term contrasts sharply with the uniqueness of the Einstein kinetic term. One might have hoped to use universal coupling as a tie-breaking criterion for choosing among theories that are equally satisfactory on more crucial grounds (such as lacking ghosts and having a smooth massless limit). But the ubiquity of universal coupling implies that the criterion does not favor any particular theories among those with the Einstein kinetic term.     

Norming algebras and automatic complete boundedness of isomorphisms of operator algebras

We combine the notion of norming algebra introduced by Pop, Sinclair and Smith with a result of Pisier to show that if and are operator algebras, then any bounded epimorphism of onto is completely bounded provided that contains a norming -subalgebra. We use this result to give some insights into Kadison's Similarity Problem: we show that every faithful bounded homomorphism of a -algebra on a Hilbert space has completely bounded inverse, and show that a bounded representation of a -algebra is similar to a -representation precisely when the image operator algebra -norms itself. We give two applications to isometric isomorphisms of certain operator algebras. The first is an extension of a result of Davidson and Power on isometric isomorphisms of CSL algebras. Secondly, we show that an isometric isomorphism between subalgebras of -diagonals () satisfying extends uniquely to a -isomorphism of the -algebras generated by and ; this generalizes results of Muhly-Qiu-Solel and Donsig-Pitts.

     

Rate constants for the reaction of OH radicals with a series of alkanes and alkenes at 299 ± 2 K

Using methyl nitrite photolysis in air as a source of hydroxyl radicals, relative rate constants for the reaction of OH radicals with a series of alkanes and alkenes have been determined at 299 ± 2 K. The rate constant ratios obtained are: relative to n-hexane = 1.00, neopentane 0.135 ± 0.007, n-butane 0.453 ± 0.007, cyclohexane 1.32 ± 0.04; relative to cyclohexane = 1.00, n-butane 0.341 ± 0.002, cyclopentane 0.704 ± 0.007, 2,3-dimethylbutane 0.827 ± 0.004, ethene 1.12 ± 0.05; relative to propene = 1.00, 2-methyl-2-butene 3.43 ± 0.13, isoprene 3.81 ± 0.17, 2,3-dimethyl-2-butene 4.28 ± 0.21. These relative rate constants are placed on an absolute basis using previous absolute rate constant data and are compared and discussed with literature data.     

Infrared absorptivity of the 9.6 μm ozone band as a function of spectral resolution and abundance

The i.r. absorptivity of the R-branch maximum (9.48 μm) of gaseous ozone was determined at 25°C as a function of spectral resolution and absorbance a/a total pressure of 735 torr of dry air. Ozone samples produced by a high voltage discharge in oxygen, and measured accurately by either a pressure or volume change, were spectroscopically measured in a 57741. environmental chamber at paths up to 69.17 m. A linear relation between spectral slit (Δv) and the ratio of the absorbances (R_v/p) of the observed absorption minimum between the R and Q branches to the absorption maximum of the R-branch was found for cm^-1 < Δv < 10cm^-1 and for absorption up to 48%. The i.r. absorptivity varied approx. 20% (from 3.9 to 4.8 cm^-1 STP) over the range of values for R_v/p studied. Absorptivity was weakly dependent on ozone abundance (w) for w?0.03 cm STP.     

Experimental investigation of chamber-dependent radical sources

While environmental chamber data have been widely used to generate and validate computer models of the chemistry occurring in polluted atmospheres, the effects of the chambers on the gas-phase chemistry being studied have been poorly characterized. In order to investigate such chamber effects, a series of NO_x—air irradiations, with trace levels of organics present to monitor OH radical concentrations, have been carried out in four different environmental chambers (ranging in volume from ～100 to 40,000 L) at varying temperatures, humidities, pressures, and reaction conditions. In addition, a number of control experiments have been carried out to validate the technique for measuring OH radical levels in these irradiations. The data show that unknown sources of OH radicals are present in all of the chambers studied. The data are consistent with the presence of two distinct radical sources: (1) the photolysis of initially present HONO, whose importance increases with increasing NO₂/NO concentration ratios, but which is a minor contributor to the overall radical flux after 30–60 min of irradiation, and (2) a constant (for these NO_x—air irradiations) radical source which dominates beyond approximately the first 60 min of irradiation. The radical input rates, after the first ∽30–60 min of irradiation, are independent of the NO concentration, increase with increasing temperature, humidity, and NO₂ concentration, are proportional to light intensity, and are dependent on the chamber employed. Although the exact nature of this radical source is still undetermined, results of experiments reported here allow a number of possible mechanisms to be ruled, out, and these are discussed.     

A Concise and Scalable Strategy for the Total Synthesis of Dictyodendrin B Based on Sequential C?H Functionalization

A sequential C H functionalization strategy for the synthesis of the marine alkaloid dictyodendrin B is reported. Our synthesis begins from commercially available 4‐bromoindole and involves six direct functionalizations around the heteroarene core as part of a gram‐scale strategy towards the natural product.     

Multiwafer zinc diffusion in an OMVPE reactor

We study diffusion of zinc into InP in a multiwafer OMVPE reactor using dimethylzinc as the diffusant source. The resulting diffusion profiles are measured by electrochemical capacitance–voltage profiling and by secondary ion mass spectrometry and compared with cleaved cross-sections imaged by scanning electron microscopy. Very good uniformity of the diffusion profile is achieved, with variation across a 3 in. wafer as little as 5%. The dependence of the diffusion depth and Zn concentration on the diffusion temperature, partial pressure of dimethylzinc, and diffusion time are reported. We observe an enhancement of the diffusion depth in area-selective diffusion of planar devices, compared to the depth obtained for blanket diffusion.     

First Monte-Carlo modelling of global beryllium migration in ITER using ERO2.0

ERO2.0 is a recently developed Monte-Carlo code for modelling global erosion and redeposition in fusion devices. We report here on the code's application to ITER for studying the erosion of the beryllium (Be) first wall armour under burning plasma steady state diverted conditions. An important goal of the study is to provide synthetic signals for the design of two key diagnostics: the main chamber visible spectroscopy and the laser in-vessel viewing systems. The simulations are performed using toroidally symmetric plasma backgrounds obtained by combining SOLPS simulations extended to the wall using the OSM-EIRENE-DIVIMP edge code package. These are then further combined with a shadowing model using magnetic field line tracing to provide a three-dimensional correction for the flux patterns. The resulting plasma wetted area, which amounts to ∼10% of the total first wall area, is in excellent agreement with shadowing calculations obtained with the SMITER field line tracing code. The simulations reveal that the main Be erosion zones are located in regions intersected by the secondary separatrix, in particular the upper Be panels, which are close to the secondary X-point. For the particular high-density Q = 10 background plasma case studied here, ∼80% of the eroded Be is found to re-deposit on main chamber surfaces. The rest migrates in almost equal parts to the inner and outer divertor and is deposited close to the strike lines.     

Universally coupled massive gravity, II: Densitized tetrad and cotetrad theories

Einstein’s equations in a tetrad formulation are derived from a linear theory in flat spacetime with an asymmetric potential using free field gauge invariance, local Lorentz invariance and universal coupling. The gravitational potential can be either covariant or contravariant and of almost any density weight. These results are adapted to produce universally coupled massive variants of Einstein’s equations, yielding two one-parameter families of distinct theories with spin 2 and spin 0. The theories derived, upon fixing the local Lorentz gauge freedom, are seen to be a subset of those found by Ogievetsky and Polubarinov some time ago using a spin limitation principle. In view of the stability question for massive gravities, the proven non-necessity of positive energy for stability in applied mathematics in some contexts is recalled. Massive tetrad gravities permit the mass of the spin 0 to be heavier than that of the spin 2, as well as lighter than or equal to it, and so provide phenomenological flexibility that might be of astrophysical or cosmological use.     

Universally coupled massive gravity

We derive Einstein’s equations from a linear theory in flat space-time using free-field gauge invariance and universal coupling. The gravitational potential can be either covariant or contravariant and of almost any density weight. We adapt these results to yield universally coupled massive variants of Einstein’s equations, yielding two one-parameter families of distinct theories with spin 2 and spin 0. The Freund-Maheshwari-Schonberg theory is therefore not the unique universally coupled massive generalization of Einstein’s theory, although it is privileged in some respects. The theories we derive are a subset of those found by Ogievetsky and Polubarinov by other means. The question of positive energy, which continues to be discussed, might be addressed numerically in spherical symmetry. We briefly comment on the issue of causality with two observable metrics and the need for gauge freedom and address some criticisms by Padmanabhan of field derivations of Einstein-like equations along the way. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 2, pp. 311–336, May, 2007.