Basic Problems of Conservative Approaches to a Theory of Quantum Gravity
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sic Problems of Conservative Approaches to a Theory of Quantum Gravity B. N. Latosha, b, c, * aUniversity
of Sussex, Brighton, BN1 9QH, United Kingdom Dubna State University, Dubna, Moscow oblast, 141982 Russia c Joint Institute for Nuclear Research, Bogolyubov Laboratory of Theoretical Physics, Dubna, 141980 Russia *e-mail: [email protected] b
Received January 16, 2020; revised February 27, 2020; accepted February 27, 2020
Abstract—A review of most basic problems is presented, which arise with application of standard approaches for developing a theory of quantum gravity. The major part of the work is dedicated to problems of perturbative quantization, based on the continual integral method. The problems of the canonical quantization program are discussed in the context of its application to the theory of gravity. A brief discussion of applying methods of effective field theory in quantum gravity is presented. DOI: 10.1134/S1063779620050056
1. INTRODUCTION The development of the theory of quantum gravity is rightfully considered as one of the most fundamental tasks of the modern theoretical physics. It can be traced back to the beginning of the last century and arises simultaneously with the general relativity theory (GRT). Einstein, himself, understood the necessity of developing a separate theory of the gravitational interaction for quantum systems; so, even in 1916 [1] he wrote the following1: “Gleichwohl müßten die Atome zufolge der inneratomischen Elektronenbewegung nicht nur elektromagnetische, sondern such Gravitationsenergie ausstrahlen, wenn auch in winzigem Betrage. Da dies in Wahrheit in der Natur nicht zutreffen dürfte, so seheint es, daß die Quantentheorie nicht nur die Maxwellsehe Elektrodynamik, sondern auch die neue Gravitationstheorie wird modifziren müssen.” The development of ideas on quantum theory and its application for describing the gravitational interaction led to the development of many sophisticated techniques and models, such as the AdS/CFT correspondence, models with complementary measurements, loop quantum gravity, supergravity, and the theory of superstrings. A detailed review of the historical development of ideas on quantum gravity together with 1 “Nevertheless,
atoms, following the laws of electron motion, should radiate not only the electromagnetic, but also gravitational energy, if only in small amounts. Since in reality, this may not occur in nature, seemingly, the quantum theory should change not only Maxwell equations, but also equations of gravitational theory.”
a discussion of the genealogy of modern approaches are given in [2, 3]. The great progress achieved in this area, paradoxically, is rather poorly described in the modern literature. A significant number of books, otherwise dedicated to the problem of quantum gravity, namely [2, 4–13], do not cover the most basic problems, precluding the construction of a theory of quantum gravity using the standard methods of quantum field theory (QFT). As far as we know, in the context of the modern QFT, these problems are cov
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