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This volume contains the Proceedings of 'Quantum Gravity': a series of qualified lectures of most outstanding scientists given during the XIV Course of the International School of Cosmology and Gravitation. As usual of that School, the Course was conceived for researchers at different levels of scientific maturity ranging from post-doctorate research students to well established research workers: then in every lecture you can find an introduction where a review and analysis of the main mathematical, physical and epistemological difficulties encountered at the formulations of relativistic quantum theories are expounded, ranging from relativistic quantum mechanics and quantum field theory in Minkowski and in curved space-time to the various canonical and covariant approaches to quantum gravity.
This monograph presents the latest findings from a long-term research project intended to identify the physics behind Quantum Mechanics. A fundamental theory for quantum mechanics is constructed from first physical principles, revealing quantization as an emergent phenomenon arising from a deeper stochastic process. As such, it offers the vibrant community working on the foundations of quantum mechanics an alternative contribution open to discussion. The book starts with a critical summary of the main conceptual problems that still beset quantum mechanics. The basic consideration is then introduced that any material system is an open system in permanent contact with the random zero-point radiation field, with which it may reach a state of equilibrium. Working from this basis, a comprehensive and self-consistent theoretical framework is then developed. The pillars of the quantum-mechanical formalism are derived, as well as the radiative corrections of nonrelativistic QED, while revealing the underlying physical mechanisms. The genesis of some of the central features of quantum theory is elucidated, such as atomic stability, the spin of the electron, quantum fluctuations, quantum nonlocality and entanglement. The theory developed here reaffirms fundamental scientific principles such as realism, causality, locality and objectivity.
The plausible relativistic physical variables describing a spinning, charged and massive particle are, besides the charge itself, its Minkowski (four) po sition X, its relativistic linear (four) momentum P and also its so-called Lorentz (four) angular momentum E # 0, the latter forming four trans lation invariant part of its total angular (four) momentum M. Expressing these variables in terms of Poincare covariant real valued functions defined on an extended relativistic phase space [2, 7J means that the mutual Pois son bracket relations among the total angular momentum functions Mab and the linear momentum functions pa have to represent the commutation relations of the Poincare algebra. On any such an extended relativistic phase space, as shown by Zakrzewski [2, 7], the (natural?) Poisson bracket relations (1. 1) imply that for the splitting of the total angular momentum into its orbital and its spin part (1. 2) one necessarily obtains (1. 3) On the other hand it is always possible to shift (translate) the commuting (see (1. 1)) four position xa by a four vector ~Xa (1. 4) so that the total angular four momentum splits instead into a new orbital and a new (Pauli-Lubanski) spin part (1. 5) in such a way that (1. 6) However, as proved by Zakrzewski [2, 7J, the so-defined new shifted four a position functions X must fulfill the following Poisson bracket relations: (1.
The first part of a two-volume set concerning the field of Clifford (geometric) algebra, this work consists of thematically organized chapters that provide a broad overview of cutting-edge topics in mathematical physics and the physical applications of Clifford algebras. algebras and their applications in physics. Algebraic geometry, cohomology, non-communicative spaces, q-deformations and the related quantum groups, and projective geometry provide the basis for algebraic topics covered. Physical applications and extensions of physical theories such as the theory of quaternionic spin, a projective theory of hadron transformation laws, and electron scattering are also presented, showing the broad applicability of Clifford geometric algebras in solving physical problems. Treatment of the structure theory of quantum Clifford algebras, the connection to logic, group representations, and computational techniques including symbolic calculations and theorem proving rounds out the presentation.
This book provides an up-to-date understanding of the progress and current problems of the interplay of nonlocality in the classical theories of gravitation and quantum theory. These problems lie on the border between general relativity and quantum physics, including quantum gravity.
The past twenty years have seen a number of breakthroughs in astrophysics and cosmology, some of which have been awarded Nobel prizes. These physics triumphs highlight the fact that while students need a solid grounding in the fundamentals of astrophysics and cosmology, sight of the basics of the fundamental interactions in physics must not be lost. This book presents papers based on lectures given at the 200th Course of the International School of Physics “Enrico Fermi”, on Gravitation and Cosmology, held in Varenna, Italy, from 3 - 12 July 2017. The aim of the school was to expose students to state-of-the-art research in the field of gravitational waves and cosmology, from both a theoretical and experimental point of view. Lectures were organized in such a way as to foster interaction between the two communities, and a wide range of topics was addressed. In the gravitational waves section, topics covered include experimental issues connected with gravitational wave detection and the new field of multi-messenger astronomy, as well as more astrophysical aspects. In the section on cosmology, there are contributions on the early universe, on the cosmic microwave background (CMB) and on redshift surveys. Other areas covered include a review of inflationary scenarios; the non-Gaussian features of primordial density fluctuations; and the physical mechanisms responsible for the spectral distortions of the blackbody spectrum of the CMB. The book provides an overview of important research developments and will be of interest to all students of gravitation and cosmology.
The purpose of this meeting was to cover selected topics of high current interest in the interplay between cosmology and fundamental physics. It brought together physicists, astrophysicists and astronomers and allowed easy and fruitful mutual contacts and communication among them. Topics covered this year include: phase transitions in cosmology and evolution out of the equilibrium of quantum fields, fundamental strings and cosmic strings in cosmology, dark matter and large scale structure, black holes and quantum gravity.
This book collects selected papers written by invited and plenary speakers of the 15th International Congress on Mathematical Physics (ICMP) in the aftermath of the conference. In extensive review articles and expository texts as well as advanced research articles the world leading experts present the state of the art in modern mathematical physics. New mathematical concepts and ideas are introduced by prominent mathematicalphysicists and mathematicians, covering among others the fields of Dynamical Systems, Operator Algebras, Partial Differential Equations, Probability Theory, Random Matrices, Condensed Matter Physics, Statistical Mechanics, General Relativity, Quantum Mechanics, Quantum Field Theory, Quantum Information and String Theory. All together the contributions in this book give a panoramic view of the latest developments in mathematical physics. They will help readers with a general interest in mathematical physics to get an update on the most recent developments in their field, and give a broad overview on actual and future research directions in this fascinating and rapidly expanding area.
These proceedings contain lecture notes on computer algebra, cosmological models, quantum cosmology, and black hole physics. Several research articles which cover different aspects of classical cosmology, exact solutions to Einstein's equations, and quantum field theory are also included.