Bøker i Fundamental Theories of Physics-serien

This volume commemorates the scientific contributions of Detlef Dürr (1951¿2021) to foundational questions of physics. It presents new contributions from his former students, collaborators, and colleagues about their current research on topics inspired or influenced by Dürr. These topics are drawn from physics, mathematics, and philosophy of nature, and concern interpretations of quantum theory, new developments of Bohmian mechanics, the role of typicality, quantum physics in relativistic space-time, classical and quantum electrodynamics, and statistical mechanics. The volume thus also gives a snapshot of present research in the foundations of physics.

This book addresses research challenges in the rapidly developing area of nonequilibrium thermodynamics and fluctuation kinetics. This cross-disciplinary field comprises various topics, ranging from fundamental problems of nonequilibrium statistical mechanics and thermodynamics to multiple applications in plasma, fluid mechanics, nonlinear science, systems of dissipative particles, and high-Q resonators. The purpose of this book is to bring together world-leading experts in the above fields to initiate a cross-fertilization among these active research areas. The book is dedicated to and honours the memory of Professor Slava Belyi who passed away unexpectedly on May 20, 2020. He was pioneering the theory of nonequilibrium fluctuations, in particular the application of the Callen-Welton fluctuation-dissipation theorem to nonequilibrium systems and its generalization. This and related problems also feature in the book.

Our vast Universe is filled with an enormous amount of matter and energy, which are the source of large gravitational potentials affecting all physical phenomena. Because this fact about the size and contents of the Universe was not known when our fundamental theories of dynamics and relativity were completed by the 1920s, the current theories - based as they are in empty space - fail to incorporate cosmic gravity. Though the current theories are consistent with the majority of empirical facts, there are some crucial discrepancies, which demand a drastic shift to a cosmic gravitational paradigm for the theories of relativity and dynamics. The book is a detailed and widely accessible account of this paradigm, called Cosmic Relativity, supported by ample empirical evidence. It is established that all motional relativistic effects are cosmic gravitational effects. The new theory of Cosmic Relativity solves and answers all outstanding questions and puzzles about dynamics and relativity.

To understand phenomena in nature, it is important to focus not only on properties of stationary states, but also their changes in time, that is, the dynamics between bistable states. This book reviews the mechanics of first-order phase transitions and discusses relaxation and collapses of metastable states from various viewpoints, including Kramers' method for the lifetime of metastability, Langer's analysis on the singularity, effects of thermal fluctuation studied by Neel and Brown, and eigenvalue structures of the transfer-matrix for the phase transitions. The book also goes into the mechanics of metastability in quantum systems from the viewpoints of the eigenvalue problem of the Hamiltonian and the Liouvillian for a dynamical process and discusses relations between quantum tunneling processes and metastability therein. Lastly, the coercivity of magnets consisting of an ensemble of grains is reviewed.The book is beneficial for those new in the field as a primer on first-order phase transition from modern perspectives. The comprehensive content offers overviews of related topics and allows readers to quickly catch up with developments in the field.

This book offers the first systematic review of the structuralism of physical theories. Particular emphasis is placed on the inclusion of empirical imprecision into formal reconstructions of theories. The proposed measure of imprecision allows for a topological comparison of theories. Considering the ongoing debates on the nature of the thermodynamic limit in statistical mechanics, as well as on limit relations between classical and quantum mechanics, the author asserts that the Bourbaki-style structuralism, together with E. Scheibe's theory of reduction, is the best choice for reconstructing and analyzing the related questions of reduction and emergence. Readers will appreciate the critical overview of the main positions in philosophy of science, examined with particular attention to their applicability to current problems of fundamental theories of physics.

This book deals with an original contribution to the hypothetical missing link unifying the two fundamental branches of physics born in the twentieth century, General Relativity and Quantum Mechanics. Namely, the book is devoted to a review of a "covariant approach" to Quantum Mechanics, along with several improvements and new results with respect to the previous related literature. The first part of the book deals with a covariant formulation of Galilean Classical Mechanics, which stands as a suitable background for covariant Quantum Mechanics. The second part deals with an introduction to covariant Quantum Mechanics. Further, in order to show how the presented covariant approach works in the framework of standard Classical Mechanics and standard Quantum Mechanics, the third part provides a detailed analysis of the standard Galilean space-time, along with three dynamical classical and quantum examples. The appendix accounts for several non-standard mathematical methods widely used in the body of the book.

This book presents a comprehensive account of the renormalization-group (RG) method and its extension, the doublet scheme, in a geometrical point of view. It extract long timescale macroscopic/mesoscopic dynamics from microscopic equations in an intuitively understandable way rather than in a mathematically rigorous manner and introduces readers to a mathematically elementary, but useful and widely applicable technique for analyzing asymptotic solutions in mathematical models of nature. The book begins with the basic notion of the RG theory, including its connection with the separation of scales. Then it formulates the RG method as a construction method of envelopes of the naive perturbative solutions containing secular terms, and then demonstrates the formulation in various types of evolution equations. Lastly, it describes successful physical examples, such as stochastic and transport phenomena including second-order relativistic as well as nonrelativistic fluid dynamics with causality and transport phenomena in cold atoms, with extensive numerical expositions of transport coefficients and relaxation times. Requiring only an undergraduate-level understanding of physics and mathematics, the book clearly describes the notions and mathematical techniques with a wealth of examples. It is a unique and can be enlightening resource for readers who feel mystified by renormalization theory in quantum field theory.

This self-contained monograph provides a mathematically simple and physically meaningful model which unifies gravity, electromagnetism, optics and even some quantum behavior. The simplicity of the model is achieved by working in the frame of an inertial observer and by using a physically meaningful least action principle.The authors introduce an extension of the Principle of Inertia. This gives rise to a simple, physically meaningful action function. Visualizations of the geometryare obtained by plotting the action function. These visualizations may be used to compare the geometries of different types of fields. Moreover, a new understanding of the energy-momentum of a field emerges.The relativistic dynamics derived here properly describes motion of massive and massless objects under the influence of a gravitational and/or an electromagnetic field, and under the influence of isotropic media.The reader will learn how to compute theprecession of Mercury, the deflection of light, and the Shapiro time delay. Also covered is the relativistic motion of binary stars, including the generation of gravitational waves, a derivation of Snell's Law and a relativistic description of spin. We derive a complex-valued prepotential of an electromagnetic field. The prepotential is similar to the wave function in quantum mechanics. The mathematics is accessible to students after standard courses in multivariable calculus and linear algebra. For those unfamiliar with tensors and the calculus of variations, these topics are developed rigorously in the opening chapters. The unifying model presented here should prove useful to upper undergraduate and graduate students, as well as to seasoned researchers.

This book presents a collection of novel contributions and reviews by renowned researchers in the foundations of quantum physics, quantum optics, and neutron physics. It is published in honor of Michael Horne, whose exceptionally clear and groundbreaking work in the foundations of quantum mechanics and interferometry, both of photons and of neutrons, has provided penetrating insight into the implications of modern physics for our understanding of the physical world. He is perhaps best known for the Clauser-Horne-Shimony-Holt (CHSH) inequality. This collection includes an oral history of Michael Horne's contributions to the foundations of physics and his connections to other eminent figures in the history of the subject, among them Clifford Shull and Abner Shimony.

This book presents the fundamentals of stochastic thermodynamics, one of the most central subjects in non-equilibrium statistical mechanics. It also explores many recent advances, e.g., in information thermodynamics, the thermodynamic uncertainty relation, and the trade-off relation between efficiency and power.The content is divided into three main parts, the first of which introduces readers to fundamental topics in stochastic thermodynamics, e.g., the basics of stochastic processes, the fluctuation theorem and its variants, information thermodynamics, and large deviation theory. In turn, parts two and three explore advanced topics such as autonomous engines (engines not controlled externally) and finite speed engines, while also explaining the key concepts from recent stochastic thermodynamics theory that are involved.To fully benefit from the book, readers only need an undergraduate-level background in statistical mechanics and quantum mechanics; no backgroundin information theory or stochastic processes is needed. Accordingly, the book offers a valuable resource for early graduate or higher-level readers who are unfamiliar with this subject but want to keep up with the cutting-edge research in this field. In addition, the author¿s vivid descriptions interspersed throughout the book will help readers grasp ¿living¿ research developments and begin their own research in this field.

The classical and quantum dynamics of conservative systems governs the behavior of much of the world around us - from the dynamics of galaxies to the vibration and electronic behavior of molecules and the dynamics of systems formed from or driven by laser radiation. Most conservative dynamical systems contain some degree of chaotic behavior, ranging from a self-similar mixture of regular and chaotic motion, to fully developed chaos. This chaotic behavior has a profound effect on the dynamics.This book combines mathematical rigor with examples that illuminate the dynamical theory of chaotic systems. The emphasis of the 3rd Edition is on topics of modern interest, including scattering systems formed from molecules and nanoscale quantum devices, quantum control and destabilization of systems driven by laser radiation, and thermalization of condensed matter systems. The book is written on a level accessible to graduate students and to the general research community.

continues with a detailed discussion of area-preserving maps, integrable quantum systems, spectral properties, path integrals, and periodically driven systems;

This book is a tribute to the scientific legacy of GianCarlo Ghirardi, who was one of the most influential scientists in the field of modern foundations of quantum theory.

Silvia Bianchi and Claus Kiefer Introduction.- Jeremy Butterfield and Sebastian de Haro  On Gauge, Symmetry and Duality.- Gabriel Catren On Gauge Symmetries, Indiscernibilities, and Groupoid-Theoretical Identities .- Laura Covi Gauge fields in cosmology.- Silvia De Bianchi Weyl''s Raum-Zeit-Materie and the Philosophy of Science.- Dennis Dieks Hermann Weyl, Philosophy and Gauge.- Friedrich Hehl The conserved energy-momentum current of matter as the basis for the gauge theory of gravitation.- Claus Kiefer Space, Time, Matter in Quantum Gravity.- Thomas Ryckman Hermann Weyl: symbolic construction from the purely infinitesimal & gauge invariance.- Carlo Rovelli Gauge is not mathematical redundancy.- Erhard Scholz Gauging the spacetime metric -- looking back and forth a century later.- Thomas Sch├╝cker  The gauge theoretical underpinnings of general relativity.- Christian Steinwachs Higgs field in cosmology.- Norbert Straumann Hermann Weyl''s Space-Time Geometry and the Origin of Gauge Theory 100 Years ago.- Gerard ''t Hooft Past and Future of Gauge Theory.- Francesca Vidotto Loop Quantum Gravity: a general-covariant lattice gauge theory.- Christof Wetterich Scale symmetry in Quantum Gravity and cosmology.

This book presents a multidisciplinary guide to gauge theory and gravity, with chapters by the world¿s leading theoretical physicists, mathematicians, historians and philosophers of science. The contributions from theoretical physics explore e.g. the consistency of the unification of gravitation and quantum theory, the underpinnings of experimental tests of gauge theory and its role in shedding light on the relationship between mathematics and physics. In turn, historians and philosophers of science assess the impact of Weyl¿s view on the philosophy of science. Graduate students, lecturers and researchers in the fields of history of science, theoretical physics and philosophy of science will benefit from this book by learning about the role played by Weyl¿s Raum-Zeit-Materie in shaping several modern research fields, and by gaining insights into the future prospects of gauge theory in both theoretical and experimental physics. Furthermore, the book facilitates interdisciplinary exchange and conceptual innovation in tackling fundamental questions about our deepest theories of physics. Chapter ¿Weyl¿s Raum-Zeit-Materie and the Philosophy of Science¿ is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com

This book is a tribute to the scientific legacy of GianCarlo Ghirardi, who was one of the most influential scientists in the field of modern foundations of quantum theory.

This book provides a unique survey displaying the power of Riccati equations to describe reversible and irreversible processes in physics and, in particular, quantum physics. The Riccati equation, a nonlinear equation that can be linearized, has the potential to link these two worlds when applied to complex quantities.

The focus is on getting a mathematically sound connection between causal fermion systems and physical systems in Minkowski space.The book is intended for graduate students entering the field, and is furthermore a valuable reference work for researchers in quantum field theory and quantum gravity.

This book describes a relativistic quantum theory developed by the author starting from the E.C.G. This theory is able to provide solutions for some of the fundamental problems encountered in early attempts to construct a relativistic quantum theory.

geometrodynamical and loop quantum gravity approaches to quantum GR, quantum cosmology, supergravity and M-theory - are background independent in this sense.

i.e., interacting systems that have distinct classical and quantum sectors, allowing for consistent descriptions of quantum systems interacting with classical measurement devices and quantum matter fields interacting gravitationally with a classical spacetime.

This book presents a comprehensive mathematical study of the operators behind the Born-Jordan quantization scheme. Thus, Born-Jordan quantization provides the only physically consistent quantization scheme, as opposed to the Weyl quantization commonly used by physicists.

This book explains non-locality and its relationship to causality and probability in quantum theory. It displays foundational characteristics of quantum physics to understand conceptual origins of the unusual nature of quantum phenomena.

Based on the authors' everyday research experiences in the field of high-energy heavy-ion collisions, this volume bundles temperature, heat, entropy and disorder into modern physics. The main focus is thermodynamics -- the very concept of temperature, its use, and extensions.

This graduate level introduction explores the extended theories of gravity and cosmology, including variational principles, the weak-field limit, gravitational waves, and more. Complete with a consistent notation and rich references, the text unifies the existing literature in this area.

There are many excellent books on quantum theory from which one can learn to compute energy levels, transition rates, cross sections, etc. The purpose of this book is to clarify the conceptual meaning of quantum theory, and to explain some of the mathematical methods which it utilizes.