Principles Of Quantum General Relativity

This monograph explains and analyzes the principles of a quantum-geometric framework for the unification of general relativity and quantum theory. By taking advantage of recent advances in areas like fibre and superfibre bundle theory, Krein spaces, gauge fields and groups, coherent states, etc., these principles can be consistently incorporated into a framework that can justifiably be said to provide the foundations for a quantum extrapolation of general relativity. This volume aims to present this approach in a way which places as much emphasis on fundamental physical ideas as on their precise mathematical implementation. References are also made to the ideas of Einstein, Bohr, Born, Dirac, Heisenberg and others, in order to set the work presented here in an appropriate historical context.

This monograph presents a review and analysis of the main mathematical, physical and epistomological difficulties encountered at the foundational level by all the conventional formulations of relativistic quantum theories, ranging from relativistic quantum mechanics and quantum field theory in Minkowski space, to the various canonical and covariant approaches to quantum gravity. It is, however, primarily devoted to the systematic presentation of a quantum framework meant to deal effectively with these difficulties by reconsidering the foundations of these subjects, analyzing their epistemic nature, and then developing mathematical tools which are specifically designed for the elimination of all the basic inconsistencies. A carefully documented historical survey is included, and additional extensive notes containing quotations from original sources are incorporated at the end of each chapter, so that the reader will be brought up-to-date with the very latest developments in quantum field theory in curved spacetime, quantum gravity and quantum cosmology. The survey further provides a backdrop against which the new foundational and mathematical ideas of the present approach to these subjects can be brought out in sharper relief.

This book provides a complete treatise of the canonical quantisation of general relativity and the loop quantum gravity theory. Mathematical concepts are provided, so it can be read by graduate students with a basic knowledge of quantum field theory or general relativity.

This book starts from a set of common basic principles to establish the basic formalisms of all disciplines of fundamental physics, including quantum field theory, quantum mechanics, statistical mechanics, thermodynamics, general relativity, electromagnetism, and classical mechanics. Instead of the traditional pedagogic way, the author arranges the subjects and formalisms in a logical order, i.e. all the formulas are derived from the formulas before them. The formalisms are also kept self-contained. Most mathematical tools are given in the appendices. Although this book covers all the disciplines of fundamental physics, it contains only a single volume because the contents are kept concise and treated as an integrated entity, which is consistent with the motto that simplicity is beauty, unification is beauty, and thus physics is beauty.This can be used as an advanced textbook for graduate students. It is also suitable for physicists who wish to have an overview of fundamental physics.

In discussing the question of whether General Relativity Theory really needs to be quantized, a simply negative answer cannot be accepted, of course. Such an answer is not satisfying because, first, Einstein's gravitational equations connect gravity and non-gravitational matter and because, second, it can be taken for granted that non-gravitational matter has an atomic or quantum structure such that its energy-momentum tensor standing on the right-hand side of Einstein's equations is formed out of quantum operators. These two facts make it impossible to read the left-hand side of Einstein's equations as an ordinary classical function. This does not necessarily mean, however, that we must draw the conclusion that General Relativity Theory, similar to electrodynamics, could or should be quantized in a rigorous manner and that this quantization has similar consequences to quantum electrodynamics. In other words, when for reasons of consistency quantization is tried, then one has to ask whether and where the quantization procedure has a physical meaning, i.e., whether there exist measurable effects of quantum gravity. IQ accordance with these questions, we are mainly dealing with the discus sion of the principles of quantized General Relativity Theory and with the estimation of quantum effects including the question of their measurability. This analysis proves that it is impossible to distinguish between classical and quantum General Relativity Theory for the extreme case of Planck's orders of magnitude. In other words, there does not exist a physically meaningful rigorous quantization conception for Einstein's theory.

Three key aspects of quantum gravity are considered in this book: phenomenology, potential experimental aspects and foundational theory. The phenomenology is the treatment of metric quantum fluctuations as torsional curves that deviate from classical expectations. This leads to possible experimental configurations that may detect such fluctuations. Most of these proposed experiments are quantum optical measurements of subtle quantum gravity effects in the interaction of photons and atoms. The foundational discussions attempt to find an substratum to string theories, which are motivated by the phenomenological treatment. Quantum gravity is not the quantization of general relativity, but is instead the embedding of quantum theory and gravitation into a more fundamental field theoretic framework.

I am very happy to accept the translators' invitation to write a few lines of introduction to this book. Of course, there is little need to explain the author. Pauli's first famous work, his article on the theory of relativity in the Encyklopädie der Mathematischen Wissenschaften was written at the age of twenty. He afterwards took part in the development of atomic physics from the still essentially classical picture of Bohr's early work to the true quantum mechanics. Thereafter, some of his work concerned the treatment of problems in the framework of the new theory, especially his paper on the hydrogen atom following the matrix method without recourse to Schrodinger's analytic form of the theory. His greatest achievement, the exclusion principle, generally known today under his own name as the Pauli principle, that governs the quantum theory of all problems including more than one electron, preceded the basic work of Heisenberg and Schrodinger, and brought him the Nobel prize. It includes the mathematical treatment of the spin by means of the now so well known Pauli matrices. In 1929, in a paper with Heisenberg, he laid the foundation of quantum electrodynamics and, in doing so, to the whole theory of quantized wave fields which was to become the via regia of access to elementary particle physics, since here for the first time processes of generation and annihilation of particles could be described for the case of the photons.

This book starts from a set of common basic principles to establish the basic formalisms of all disciplines of fundamental physics, including quantum field theory, quantum mechanics, statistical mechanics, thermodynamics, general relativity, electromagnetism, and classical mechanics. Instead of the traditional pedagogic way, the author arranges the subjects and formalisms in a logical order, i.e. all the formulas are derived from the formulas before them. The formalisms are also kept self-contained. Most mathematical tools are given in the appendices. Although this book covers all the disciplines of fundamental physics, it contains only a single volume because the contents are kept concise and treated as an integrated entity, which is consistent with the motto that simplicity is beauty, unification is beauty, and thus physics is beauty. This can be used as an advanced textbook for graduate students. It is also suitable for physicists who wish to have an overview of fundamental physics.