Gauge approach and quantization methods in gravity theory / Ponomarev V. N., Barvinsky A. O., Obukhov Yu. N. ; Nuclear Safety Institute of the Russian Academy of Sciences -М. : Nauka, 2017. -360 p. : ill. -ISBN 978-5-02-040047-4 (bound).The book gives an overview of the geometrical gauge approach to the gravity theory and the methods of quantization of the gravitational field. Gauge-theoretic formalism (universal principle of the local invariance and the mechanism of spontaneous breaking of the gauge symmetry) forms the basis for the modern understanding of fundamental physical interactions and is successfully confirmed by the experimental discoveries of the gauge bosons and the Higgs particle. The carefully selected material of the book provides a minimal but sufficient mathematical introduction to the methods of the gauge gravitational theory, and gives a concise but exhaustive description of all specific physical consequences. In order to describe the many dramatic changes which took place recently in understanding the concepts, issues and motivations of quantum gravitational physics, a special emphasis is put on a comparison of three different quantization methods of the gravitational field -the covariant approach, the Dirac-Wheeler-DeWitt quantization and the method of Arnowitt-Deser-Misner. The basics of the canonical quantization is explained along with the detailed exposition of the path integral approach, and the introduction to the modern BRST technique is given to demonstrate the consistency of the Arnowitt-Deser-Misner and the Dirac-Wheeler-DeWitt quantization schemes. The book addresses the physicists who specialize in the gravity theory and the high-energy physics, and it can be recommended to the graduate students and senior undergraduate university students in theoretical physics and mathematics. Формализм калибровочной теории (универсальный принцип локальной инвариантности и механизм спонтанного нарушения калибровочной симметрии) лежит в основе современного понимания фундаментальных физических взаимодействий и успешно подтверждается экспе-риментальными открытиями калибровочных бозонов и частицы Хиггса. В книге дается обзор геометрического калибровочного подхода к теории гравитации и методов квантования гравита-ционного поля. Тщательно подобранный материал книги обеспечивает минимальное, но доста-точное математическое введение в методы калибровочной теории гравитации и дает краткое, но исчерпывающее описание конкретных физических следствий калибровочного подхода. Чтобы осветить многочисленные драматические изменения, произошедшие в последнее время в осмы-слении понятий, проблем и целей квантово-гравитационной физики, особое внимание уделя-ется сравнению трех различных методов квантования гравитационного поля -ковариантного подхода, квантования Дирака-Уилера-ДеВитта и метода Арновитта-Дезера-Мизнера. В книге объясняются основы канонического квантования наряду с подробным изложением формализ-ма континуальных интегралов, и дается введение в современную технику БРСТ, с тем чтобы продемонстрировать с...

Summary. The shifts of current-voltage characteristics of sodium and calcium inward currents produced by changes in the concentration of divalent cations (Mg 2+, Ca 2+, Sr 2+, Ba 2+) and in pH of the extracellular solution have been measured on isolated neurons of the mollusc Helix pomatia intracellularly perfused with potassium-free solutions. On the basis of these shifts and using Stern's theory (O. Stern, 1924, Z. Electrochem. 30:508-516), the binding constants for the ions to charged groups of the outer side of the somatic membrane and the density of the surface charges produced by these groups have been calculated. For groups located in the vicinity of sodium channels we obtained K c~=90+10, Ksr=60+ 10, K~a=25 +5 and KMg=16• at pH---7.7 and forgroups located~n the vicinity of calcium channels Kca = 67 +_ 10, Ks, = 20 +_ 5 and KBa=18_+5M -1 at pH=7.0. The same groups bind H § ions with apparent pK=6.2_+0.2 that corresponds to KH=I.6 x 106M -1. The density of fixed charges near the sodium channels is 0.17+0.05e/nm z (pH=7.7) and near the calcium channels is 0.23+0.05electrons/nm z (pH =7.0). From the comparison of the obtained values with the data about binding constants of the same ions to different negatively charged phospholipids, a suggestion is made that just the phosphatidylserine is responsible for the surface potential of the outer side of the somatic membrane. It was also shown that the presence of this potential results in a change in the concentration of carrier ions near the membrane which affects the maximal values of the corresponding transmembrane currents.

Measurements of the ion convection velocity (transverse horizontal and vertical components) from asymmetry of the lateral ion flow in the satellite frame and also of the total ion concentration were conducted in October-November 1967 from the Cosmos 184 satellite (circular orbit at 630 km, inclination 81ø2'). In this study, first the cases were selected when a reversal of the sign of the By component of the IMF had taken place during the time interval between two successive satellite passes through the equatorial ionospheric anomaly (11 cases). Systematic decreases of the near-equatorial ion density were observed after reversals from By negative to By positive. These decreases were accompanied by relative enhancements of the upward and the eastward components of the plasma drift velocity of the order of several tens of meters per second. Variations of the opposite direction were observed (though less regularly) after By reversals from positive to negative. Important vertical and horizontal plasma drift velocities appear in the irregular density variations and especially at localized ionization spikes (downward velocity relative to surrounding plasma) and dropouts (upward relative velocity). These density dropouts are very similar to the 'plasma bubbles' reported by McClure et al. (1977) and at 630 km are observed mostly when the density profile has a near-equatorial valley. It was shown by Heppner (1972) that the polar cap convection pattern depends on the sign of the By IMF component. If follows that suitably selected polar plasma drift data from Cosmos 184 can also be used to find the pairs of orbits indicating the reversals of By IMF ('inferred reversals'). Typical signatures of the plasma drift pattern in the noon region close to the southern (sunlit) dayside polar cusp were constructed from the whole set of Cosmos 184 data. These signatures indeed show high correlation with the sign of By IMF. The reversal of typical signatures on a pair of successive orbits in fact represents the direct indication of the large-scale electric field variation in the polar ionosphere/outer magnetosphere presumably induced by the reversals of By IMF (9 cases partly overlapping the 11 cases mentioned above). The two sets of data (pairs of orbits) are in general accord (with several doubtful cases but no direct contradictions) both with respect to the By sign reversal evaluation and with respect to the above-described differential variations in the latitudinal ion density profiles and in the plasma drift velocities in the equatorial ionospheric anomaly. These observations confirm the propagation of the electric field variations from polar ionosphere/outer magnetosphere down to the equatorial latitudes, as was suggested by Rastogi and Patel (1975).

Magnetic measurements of the vertical field component and of magnetic susceptibility were made within the ocean crust in Deep Sea Drilling Project Hole 395A on the Mid-Atlantic Ridge during Leg 78B. The variations in the vertical anomalous component of the field confirm the reversals of magnetization in the section described by Johnson (1979a). The reversals are shown to be very sharp, and are concluded to represent breaks in volcanism within which field reversals occurred. The continuous log of the vertical component of the field gives a far more complete and detailed view of the magnetic stratigraphy than was obtained from the minicores alone. The susceptibility log shows two positive anomalies in the upper part of the section that probably relate to the presence of serpentinite in the walls of the hole. At one of these horizons some serpentinite was recovered in the core but not at the other. The log thus provided a valuable and sensitive adjunct to the recovered samples.

A downhole magnetometer was deployed within the ocean crust for the first time in holes drilled on the south flank of the Costa Rica Rift during Deep Sea Drilling Project Legs 68 and 69. The holes in question were Holes 501, 504B, and 5O5B. The magnetometer was a three-component fluxgate and measured magnetic susceptibility, the vertical field, and two horizontal components of the field oriented relative to the dip of the drill holes. Hole 5O5B was too near the vertical for the horizontal orientation to be stable. In all holes, the anomalous field was far too intense to have been caused by induced magnetization. Most of the field is the effect of remanent magnetization. The direction of the magnetization vector changes with increasing depth in the holes, but the effect of secular field variation is difficult to distinguish from that of tectonic rotation. Large systematic deviations that may herald a reversal appear in the in-hole magnetic anomalous field vector near a depth of 200 meters in Hole 504B, but measurements were not continued in the lower part of the hole. Zones of low anomalous field intensity in Hole 504B seem to correspond to zones of brecciation.