The chapters in this monograph are contributions from the Advances in Quantum Monte Carlo symposium held at Pacifichem 2010, International Chemical Congress of Pacific Basin Societies. The symposium was dedicated to celebrate the career of James B. Anderson, a notable researcher in the field. Quantum Monte Carlo provides an ab initio solution to the Schroedinger equation by performing a random walk through configuration space in imaginary time. Benchmark calculations suggest that its most commonly-used variant, "fixed-node" diffusion Monte Carlo, estimates energies with an accuracy comparable to that of high-level coupled-cluster calculations. These two methods, each having advantages and disadvantages, are complementary "gold-standards" of quantum chemistry. There are challenges facing researchers in the field, several of which are addressed in the chapters in this monograph. These include improving the accuracy and precision of quantum Monte Carlo calculations; understanding the exchange nodes and utilizing the simulated electron distribution; extending the method to large and/or experimentally-challenging systems; and developing hybrid molecular mechanics/dynamics and Monte Carlo algorithms.

Advances in Quantum Monte Carlo confronts the challenges in quantum mechanics that have become progressively more prevalent in the last five years. This book will cover the needed advances in Quantum Monte Carlo methods including improvements and a complete range of applications. Advances in Quantum Monte Carlo will also include a complete spectrum of applications.

This book deals with underlying basic concepts in relativity. The fundamental work of Stueckelberg, who formulated a consistent relativistic classical and quantum dynamics, generalized for application to many-body systems by Horwitz and Piron (SHP theory), is explained with emphasis on its conceptual content. The two-body bound state and scattering theory are also discussed. The ideas are involved in the Lindner experiment showing interference in time and the proposed experiment of Palacios et al. searching for the persistence of entanglement at unequal times is discussed. The meaning of the Newton-Wigner position operator and the Landau-Peierls construction in terms of relativistic dynamics is given. Finally, the embedding of the SHP theory into the framework of general relativity, providing a canonical structure with particle coordinates and momenta, is studied, carrying with it new concepts in relativistic dynamics.

A discourse on time, gravity, and the universe that takes the reader through the subtleties of time, the origin of the universe, and physical evolution in Einstein's theory and its extensions. Can time and causality remain fundamental when the classical ideal of spacetime becomes a concept of limited applicability in quantum gravity? A thorough exposition on the canonical framework of Einstein's theory and its extensions reveals the synergy between gravitation and the cosmic clock of our expanding universe that renders time concrete, physical, and comprehensible. In conjunction with a paradigm shift from four-covariance to just spatial diffeomorphism invariance, causal time-ordering of the quantum state of the universe and its evolution in cosmic time become meaningful. The quantum state of the universe is the embodiment of our shared past, present, and future. The advocated framework prompts natural extensions and improvements to Einstein's theory. A salient feature is the addition of a Cotton-York term to the physical Hamiltonian. Besides bringing improved ultraviolet convergence, this radically changes the solution to the initial data problem and the quantum origin of the universe. It lends support to the quantum beginning of the universe as an exact Chern-Simons Hartle-Hawking state that features Euclidean-Lorentzian instanton tunneling. A signature of this state is that it manifests, at the lowest order approximation, scale-invariant two-point correlation function for transverse-traceless quantum metric fluctuations. This initial quantum state also implies, at the level of expectation values, a low-entropy hot smooth Robertson-Walker beginning that is in accord with Penrose's Weyl Curvature Hypothesis. Consequently, the gravitational arrow of time of increasing spatial volume and the thermodynamic second law arrow of time of increasing entropy concur as our universe expands and ages.

The book aims to give a mathematical presentation of the theory of general relativity (that is, spacetime-geometry-based gravitation theory) to advanced undergraduate mathematics students. Mathematicians will find spacetime physics presented in the definition-theorem-proof format familiar to them. The given precise mathematical definitions of physical notions help avoiding pitfalls, especially in the context of spacetime physics describing phenomena that are counter-intuitive to everyday experiences.In the first part, the differential geometry of smooth manifolds, which is needed to present the spacetime-based gravitation theory, is developed from scratch. Here, many of the illustrating examples are the Lorentzian manifolds which later serve as spacetime models. This has the twofold purpose of making the physics forthcoming in the second part relatable, and the mathematics learnt in the first part less dry. The book uses the modern coordinate-free language of semi-Riemannian geometry. Nevertheless, to familiarise the reader with the useful tool of coordinates for computations, and to bridge the gap with the physics literature, the link to coordinates is made through exercises, and via frequent remarks on how the two languages are related.In the second part, the focus is on physics, covering essential material of the 20th century spacetime-based view of gravity: energy-momentum tensor field of matter, field equation, spacetime examples, Newtonian approximation, geodesics, tests of the theory, black holes, and cosmological models of the universe.Prior knowledge of differential geometry or physics is not assumed. The book is intended for self-study, and the solutions to the (over 200) exercises are included.

The book aims to give a mathematical presentation of the theory of general relativity (that is, spacetime-geometry-based gravitation theory) to advanced undergraduate mathematics students. Mathematicians will find spacetime physics presented in the definition-theorem-proof format familiar to them. The given precise mathematical definitions of physical notions help avoiding pitfalls, especially in the context of spacetime physics describing phenomena that are counter-intuitive to everyday experiences.In the first part, the differential geometry of smooth manifolds, which is needed to present the spacetime-based gravitation theory, is developed from scratch. Here, many of the illustrating examples are the Lorentzian manifolds which later serve as spacetime models. This has the twofold purpose of making the physics forthcoming in the second part relatable, and the mathematics learnt in the first part less dry. The book uses the modern coordinate-free language of semi-Riemannian geometry. Nevertheless, to familiarise the reader with the useful tool of coordinates for computations, and to bridge the gap with the physics literature, the link to coordinates is made through exercises, and via frequent remarks on how the two languages are related.In the second part, the focus is on physics, covering essential material of the 20th century spacetime-based view of gravity: energy-momentum tensor field of matter, field equation, spacetime examples, Newtonian approximation, geodesics, tests of the theory, black holes, and cosmological models of the universe.Prior knowledge of differential geometry or physics is not assumed. The book is intended for self-study, and the solutions to the (over 200) exercises are included.

Instant Physics pulls together all the pivotal physics knowledge and thought into one concise volume. Each page contains a discrete 'cheat sheet', which tells you the most important facts in bite-sized chunks, meaning you can become an expert in an instant. From black holes to black body radiation, telescopes to microscopes, quantum mechanics to general relativity, every key figure, discovery or idea is explained with succinct and lively text and graphics. Perfect for the knowledge hungry and time poor, this collection of graphic-led lessons makes psychology interesting and accessible. Everything you need to know is here.

Somewhere near the heart of existence, shimmers the ethereal beauty of the mystery of Time. Though seemingly familiar to us all, time harbours secrets that penetrate the very deepest levels of reality, and though we feel certain in our conviction that we're swept forth upon the crest of its never-ending flow, with Einstein's discovery of relativity came what is perhaps the most stunning realisation in the entire history of scientific thought - the wondrously breathtaking revelation that in reality, there's actually no such thing as the passage of time... How can this extraordinary truth be reconciled with the reality we so surely suppose to experience? What does it mean for the very human concerns of life and death, free will, identity, and self? What should it mean for our philosophy? And how should it inform our world view? The search for answers leads through the fantastical realm of quantum physics, and the strange parallel worlds it describes, as we discover that the answers which such questions provoke, are perhaps even more profound than the questions themselves. Buried deep within the riddle of time, lies the staggering beauty of the world. As we peel back the layers to try and sneak a glimpse into eternity, we find a light shining not only upon the nature of reality, but on the nature of ourselves...

Owing to the increased accuracy requirements in fields such as astrometry and geodesy the general theory of relativity must be taken into account for any mission requiring highly accurate orbit information and for practically all observation and measurement techniques. This book highlights the confluence of Applied Mathematics, Physics and Space Science as seen from Einstein's general theory of relativity and aims to bridge the gap between theoretical and applied domains. The book investigates three distinct areas of general relativity: Exact solutions of the Einstein field equations of gravitation. Dynamics of near-Earth objects and solar system bodies. Relativistic orbitography. This book is an updated and expanded version of the author's PhD thesis which was awarded the International Astronomical Union PhD prize in Division A: Fundamental Astronomy. Included is a new introduction aimed at graduate students of General Relativity and extended discussions and results on topics in post-Newtonian dynamics and general relativistic spacecraft propagation.

This volume provides a detailed description of some of the most active areas in astrophysics from the largest scales probed by the Planck satellite to massive black holes that lie at the heart of galaxies and up to the much awaited but stunning discovery of thousands of exoplanets. It contains the following chapters: * Jean-Philippe UZAN, The Big-Bang Theory: Construction, Evolution and Status * Jean-Loup PUGET, The Planck Mission and the Cosmic Microwave Background * Reinhard GENZEL, Massive Black Holes: Evidence, Demographics and Cosmic Evolution * Arnaud CASSAN, New Worlds Ahead: The Discovery of Exoplanets Reinhard Genzel and Andrea Ghez shared the 2020 Nobel Prize in Physics "for the discovery of a supermassive compact object at the centre of our galaxy'", alongside Roger Penrose "for the discovery that black hole formation is a robust prediction of the general theory of relativity". The book corresponds to the twentieth Poincare Seminar, held on November 21, 2015, at Institut Henri Poincare in Paris. Originally written as lectures to a broad scientific audience, these four chapters are of high value and will be of general interest to astrophysicists, physicists, mathematicians and historians.

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 collates papers presented at two international conferences (held at the Australian National University in 2018 and Birkbeck College London in 2019) exploring the relationships between big history and astrobiology and their wider implications for society. These two relatively new academic disciplines aim to integrate human history with the wider history of the universe and the search for life elsewhere. The book will show that, despite differences in emphasis, big history and astrobiology share much in common, especially their interdisciplinary approaches and the cosmic and evolutionary perspectives that they both engender. Specifically, the book addresses the unified, all-embracing, nature of knowledge, the impact of big history on humanity and the world at large, the possible impact of SETI on astrobiology and big history, the cultural signature of Earth's inhabitants beyond our own planet, and the political implications of a planetary worldview. The principal readership is envisaged to comprise scholars working in the fields of astrobiology, big history and space exploration interested in forging interdisciplinary links between these diverse topics, together with educators, and a wider public, interested in the societal implications of the cosmic and evolutionary perspectives engendered by research in these fields.