Gauge approach and quantization methods in gravity theory

Abstract

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...

Gauge Structure of Teleparallel Gravity

“…The latter has a natural interpretation as the gauge theory [18] of the general affine group GA(4, R) = GL(4, R) ⋊ T 4 , the semi-direct product of the general linear group and the group of translations. The fiber bundle formulation in this case can be consistently constructed in terms of affine connections on the principal bundle of affine frames [19].…”

Exact Solutions in Poincaré Gauge Gravity Theory

“…The 10-parameter Poincaré symmetry group G = T 4 ⋊ SO(1, 3) is a semidirect product of the 4-parameter group of translations and the 6-parameter local Lorentz group, and the Yang-Mills-Utiyama-Kibble formalism can be consistently developed on a spacetime manifold [1,2]. The corresponding gravitational field potentials ("translational" and "rotational", respectively) are then naturally identified with the 1-forms of the coframe and the local Lorentz connection:…”

“…In simple terms, the gauge principle relates physical forces to the underlying symmetry groups. The corresponding Yang-Mills type formalism was developed for the internal symmetries, which form the foundation for the theories of electromagnetic, weak and strong interactions, and consistently generalized to the spacetime symmetries [1,2] which give rise to the gravitational interaction. In the current research, much attention is paid to the gauge-theoretic models based on the Poincaré group, see [3,4] for an introduction.…”

Non-Riemannian description of Robinson–Trautman spacetimes in Brans–Dicke theory of gravity

“…On the one hand, Gürsey [14] argued that Einstein's theory of general relativity as it stands incorporates Mach's Principle and detailed the reformulation of the metric as a product of a scalar density φ 2 and a tensor density. On the other hand, conformal re-scaling properties of scalar-tensor gravity theories have been further elaborated, for instance, by Deser [15] and Anderson [16].Here, we are generalising this model by considering a non-Riemannian description of spacetime where the spacetime torsion is determined by the gradient of a scalar field [17,18]. We are going to include in our discussion an arbitrary conformal scale factor of the metric as well in order to analyse the solutions in different "frames" (pictures).…”