With applications in quantum field theory, general relativity and elementary particle physics, this four-volume work studies the invariance of differential operators under Lie algebras, quantum groups and superalgebras. This third volume covers supersymmetry, including detailed coverage of conformal supersymmetry in four and some higher dimensions, furthermore quantum superalgebras are also considered. Contents Lie superalgebras Conformal supersymmetry in 4D Examples of conformal supersymmetry for D > 4 Quantum superalgebras

Of all philosophers of the 20th century, few built more bridges between academic disciplines than Karl Popper. He contributed to a wide variety of fields in addition to the epistemology and the theory of scientific method for which he is best known. This book illustrates and evaluates the impact, both substantive and methodological, that Popper has had in the natural and mathematical sciences. The topics selected include quantum mechanics, evolutionary biology, cosmology, mathematical logic, statistics, and cognitive science. The approach is multidisciplinary, opening a dialogue across scientific disciplines and between scientists and philosophers.

By focusing on the mostly used variational methods, this monograph aspires to give a unified description and comparison of various ways of constructing conserved quantities for perturbations and to study symmetries in general relativity and modified theories of gravity. The main emphasis lies on the field-theoretical covariant formulation of perturbations, the canonical Noether approach and the Belinfante procedure of symmetrisation. The general formalism is applied to build the gauge-invariant cosmological perturbation theory, conserved currents and superpotentials to describe physically important solutions of gravity theories. Meticulous attention is given to the construction of conserved quantities in asymptotically-flat spacetimes as well as in asymptotically constant curvature spacetimes such as the Anti-de Sitter space. Significant part of the book can be used in graduate courses on conservation laws in general relativity. THE SERIES: DE GRUYTER STUDIES IN MATHEMATICAL PHYSICS The series is devoted to the publication of monographs and high-level texts in mathematical physics. They cover topics and methods in fields of current interest, with an emphasis on didactical presentation. The series will enable readers to understand, apply, and develop further, with sufficient rigor, mathematical methods to given problems in physics. The works in this series are aimed at advanced students and researchers in mathematical and theoretical physics. They can also serve as secondary reading for lectures and seminars at advanced levels.

This thesis presents theoretical and numerical studies on phenomenological description of the quark gluon plasma (QGP), a many-body system of elementary particles.

The author formulates a causal theory of hydrodynamics for systems with net charges from the law of increasing entropy and a momentum expansion method. The derived equation results can be applied not only to collider physics, but also to the early universe and ultra-cold atoms.

The author also develops novel off-equilibrium hydrodynamic models for the longitudinal expansion of the QGP on the basis of these equations. Numerical estimations show that convection and entropy production during the hydrodynamic evolution are key to explaining excessive charged particle production, recently observed at the Large Hadron Collider. Furthermore, the analyses at finite baryon density indicate that the energy available for QGP production is larger than the amount conventionally assumed. "

This book consists of invited reviews written by world-renowned experts on the subject of the outskirts of galaxies, an upcoming field which has been understudied so far. These regions are faint and hard to observe, yet hide a tremendous amount of information on the origin and early evolution of galaxies. They thus allow astronomers to address some of the most topical problems, such as gaseous and satellite accretion, radial migration, and merging. The book is published in conjunction with the celebration of the end of the four-year DAGAL project, an EU-funded initial training network, and with a major international conference on the topic held in March 2016 in Toledo. It thus reflects not only the views of the experts, but also the scientific discussions and progress achieved during the project and the meeting. The reviews in the book describe the most modern observations of the outer regions of our own Galaxy, and of galaxies in the local and high-redshift Universe. They tackle disks, haloes, streams, and accretion as observed through deep imaging and spectroscopy, and guide the reader through the various formation and evolution scenarios for galaxies. The reviews focus on the major open questions in the field, and explore how they can be tackled in the future. This book provides a unique entry point into the field for graduate students and non-specialists, and serves as a reference work for researchers in this exciting new field.

This thesis provides a detailed and comprehensive description of the search for New Physics at the Large Hadron Collider (LHC) in the mono-jet final state, using the first 3.2 fb-1 of data collected at the centre of mass energy of colliding protons of 13~TeV recorded in the ATLAS experiment at LHC. The results are interpreted as limits in different theoretical contexts such as compressed supersymmetric models, theories that foresee extra-spatial dimensions and in the dark matter scenario. In the latter the limits are then compared with those obtained by other ATLAS analyses and by experiments based on completely different experimental techniques, highlighting the role of the mono-jet results in the context of dark matter searches.Lastly, a set of possible analysis improvements are proposed to reduce the main uncertainties that affect the signal region and to increase the discovery potential by further exploiting the information on the final state.

This book employs computer simulations of 'artificial' Universes to investigate the properties of two popular alternatives to the standard candidates for dark matter (DM) and dark energy (DE). It confronts the predictions of theoretical models with observations using a sophisticated semi-analytic model of galaxy formation. Understanding the nature of dark matter (DM) and dark energy (DE) are two of the most central problems in modern cosmology. While their important role in the evolution of the Universe has been well established-namely, that DM serves as the building blocks of galaxies, and that DE accelerates the expansion of the Universe-their true nature remains elusive. In the first half, the authors consider 'sterile neutrino' DM, motivated by recent claims that these particles may have finally been detected. Using sophisticated models of galaxy formation, the authors find that future observations of the high redshift Universe and faint dwarf galaxies in the Local Group can place strong constraints on the sterile neutrino scenario. In the second half, the authors propose and test novel numerical algorithms for simulating Universes with a 'modified' theory of gravity, as an alternative explanation to accelerated expansion. The authors' techniques improve the efficiency of these simulations by more than a factor of 20 compared to previous methods, inviting the readers into a new era for precision cosmological tests of gravity.

Pulsar timing is a promising method for detecting gravitational waves in the nano-Hertz band. In his prize winning Ph.D. thesis Rutger van Haasteren deals with how one takes thousands of seemingly random timing residuals which are measured by pulsar observers, and extracts information about the presence and character of the gravitational waves in the nano-Hertz band that are washing over our Galaxy. The author presents a sophisticated mathematical algorithm that deals with this issue. His algorithm is probably the most well-developed of those that are currently in use in the Pulsar Timing Array community. In chapter 3, the gravitational-wave memory effect is described. This is one of the first descriptions of this interesting effect in relation with pulsar timing, which may become observable in future Pulsar Timing Array projects. The last part of the work is dedicated to an effort to combine the European pulsar timing data sets in order to search for gravitational waves. This study has placed the most stringent limit to date on the intensity of gravitational waves that are produced by pairs of supermassive black holes dancing around each other in distant galaxies, as well as those that may be produced by vibrating cosmic strings. Rutger van Haasteren has won the 2011 GWIC Thesis Prize of the Gravitational Wave International Community for his innovative work in various directions of the search for gravitational waves by pulsar timing. The work is presented in this Ph.D. thesis.

This book offers review chapters written by invited speakers of the 3rd Session of the Sant Cugat Forum on Astrophysics - Gravitational Waves Astrophysics. All chapters have been peer reviewed. The book goes beyond normal conference proceedings in that it provides a wide panorama of the astrophysics of gravitational waves and serves as a reference work for researchers in the field.

This book is an introduction to the theories of Special and General Relativity. The target audience are physicists, engineers and applied scientists who are looking for an understandable introduction to the topic - without too much new mathematics. The fundamental equations of Einstein's theory of Special and General Relativity are derived using matrix calculus, without the help of tensors. This feature makes the book special and a valuable tool for scientists and engineers with no experience in the field of tensor calculus. In part I the foundations of Special Relativity are developed, part II describes the structure and principle of General Relativity. Part III explains the Schwarzschild solution of spherical body gravity and examines the "Black Hole" phenomenon. Any necessary mathematical tools are user friendly provided, either directly in the text or in the appendices.

One of the open challenges in fundamental physics is to combine Einstein's theory of general relativity with the principles of quantum mechancis. In this thesis, the question is raised whether metric quantum gravity could be fundamental in the spirit of Steven Weinberg's seminal asymptotic safety conjecture, and if so, what are the consequences for the physics of small, possibly Planck-size black holes? To address the first question, new techniques are provided which allow, for the first time, a self-consistent study of high-order polynomial actions including up to 34 powers in the Ricci scalar. These novel insights are then exploited to explain quantum gravity effects in black holes, including their horizon and causal structure, conformal scaling, evaporation, and the thermodynamics of quantum space-time. Results indicate upper limits on black hole temperature, and the existence of small black holes based on asymptotic safety for gravity and thermodynamical arguments.

Despite the rapidly expanding ambit of physical research and the continual appearance of new branches of physics, the main thrust in its development has been the attempt at a theoretical synthesis of the entire body of physical knowledge. Vladimir Vizgin's work presents perhaps the first systematic historico-scientific study of the formation and development of the unified field theories in the general context of 20th century physics. Concentrating on the first three decades of the century and drawing extensively on Russian sources, the author analyses the first successes, failures and paths of further development of the unified field theories. He presents the evolution of these theories as a process of interaction/competition between the geometric field and quantum research programs, and ascertains the relevance of these theories for fundamental concepts in modern field theory.

This book presents the proceedings of the 2nd Karl Schwarzschild Meeting on Gravitational Physics, focused on the general theme of black holes, gravity and information.Specialists in the field of black hole physics and rising young researchers present the latest findings on the broad topic of black holes, gravity, and information, highlighting its applications to astrophysics, cosmology, particle physics, and strongly correlated systems.

This work is an introduction to the totality of the metaphysical philosophy of nature of Hedwig Conrad-Martius (1888-1966). Her own training and inclination as a realist phenomenologist enables a unique perspective on central issues in modern and contemporary (twentieth century) theoretical biology and physics. Here we find novel theories of, e.g., space and time, as well as development and evolution. This work is thus of interest to anyone studying the history of the phenomenological movement as well as religious cosmology. The philosophical basis for this cosmology is Conrad-Martius' "realontology" which is a phenomenological account of the essence of appearing reality. The full elaboration of the modes of appearing of what is real enables the unfolding of an analogical theory of "selfness" within the order of nature culminating in an account of the coming to be of humans, for whom there is an essentially distinctive world- and self-manifestation for which she reserves the term "spirit." Key to her position is the revival of ancient metaphysical themes in new transformed guises, especially potentiality and entelechy. Nature's status, as a self-actuation of world-constituting essence-entelechies, places Conrad-Martius in the middle of philosophical-theological discussions of, e.g., the hermeneutical mandate of demythologization as well as the nature of evolution. Of special interest is her insistence on both nature's self-actuating and evolving powers and a robust theory of creation.

This book describes the endeavour to relate the particle spectrum with representations of operational electroweak spacetime, in analogy to the atomic spectrum as characterizing representations of hyperbolic space. The spectrum of hyperbolic position space explains the properties of the nonrelativistic atoms; the spectrum of electroweak spacetime is hoped to explain those of the basic interactions and elementary particles. In this book, the theory of operational symmetries is developed from the numbers, from Plato's and Kepler's symmetries over the simple Lie groups to their applications in nonrelativistic, special relativistic and general relativistic quantum theories with the atomic spectrum for hyperbolic position and, in first attempts, the particle spectrum for electroweak spacetime. The standard model of elementary particles and interactions is characterized by a symmetry group. In general, as initiated by Weyl and stressed by Heisenberg, quantum theory can be built as a theory of operation groups and their unitary representations. In such a framework, time, position and spacetime is modeled by equivalence classes of symmetry groups. For a unification on this road, the quest is not for a final theory with a basic equation for basic particles, but for the basic operation group and its representations.

Hans Reichenbach, a philosopher of science who was one of five students in Einstein's first seminar on the general theory of relativity, became Einstein's bulldog, defending the theory against criticism from philosophers, physicists, and popular commentators. This book chronicles the development of Reichenbach's reconstruction of Einstein's theory in a way that clearly sets out all of its philosophical commitments and its physical predictions as well as the battles that Reichenbach fought on its behalf, in both the academic and popular press. The essays include reviews and responses to philosophical colleagues, such as Moritz Schlick and Hugo Dingler; polemical discussions with physicists Max Born and D. C. Miller; as well as popular articles meant to clarify aspects of Einstein's theories and set out their philosophical ramifications for the layperson. At a time when physics and philosophy were both undergoing revolutionary changes in content and method, this book is a window into the development of scientific philosophy and the role of the philosopher.

This textbook offers a readily comprehensible introduction to classical Newtonian gravitation, which is fundamental for an understanding of classical mechanics and is particularly relevant to Astrophysics. The opening chapter recalls essential elements of vectorial calculus, especially to provide the formalism used in subsequent chapters. In chapter two Classical Newtonian gravity theory for one point mass and for a generic number N of point masses is then presented and discussed. The theory for point masses is naturally extended to the continuous case. The third chapter addresses the paradigmatic case of spherical symmetry in the mass density distribution (central force), with introduction of the useful tool of qualitative treatment of motion. Subsequent chapters discuss the general case of non-symmetric mass density distribution and develop classical potential theory, with elements of harmonic theory, which is essential to understand the potential development in series of the gravitational potential, the subject of the fourth chapter. Finally, in the last chapter the specific case of motion of a satellite around the earth is considered. Examples and exercises are presented throughout the book to clarify aspects of the theory. The book is aimed at those who wish to progress further beyond an initial bachelor degree, onward to a master degree, and a PhD. It is also a valuable resource for postgraduates and active researchers in the field.

Tackling galactic evolution in a truly novel way, this outstanding thesis statistically explores the long-term evolution of galaxies, using recent theoretical breakthroughs that explicitly account for their self-gravity. While treating processes statistically, the astrophysical differences on each scale are also captured. As the archetype of self-amplified diffusion, the implications of the thesis go far beyond astrophysics. Gravity is the driving force in galaxies, from their far outskirts to their innermost cores. These "extended kinetic theories" offer unique physical insights into the competing dynamical processes at play, complementing N-body approaches. The thesis successfully gauges the role of nature and nurture in establishing the galaxies' observed properties, using kinetic equations to capture both sources of fluctuations. Further, it shows how secular diffusion shapes the phase space structure of cold stellar disks. The thesis subsequently determines the characteristic timescales and examines the signatures of secular evolution in this framework on two scales: from the kinetic evolution in galactic disks and their thickening via giant molecular clouds; all the way down to the stellar resonant relaxation of the central cluster and its black hole.

This book focuses on a critical discussion of the status and prospects of current approaches in quantum mechanics and quantum field theory, in particular concerning gravity. It contains a carefully selected cross-section of lectures and discussions at the seventh conference "Progress and Visions in Quantum Theory in View of Gravity" which took place in fall 2018 at the Max Planck Institute for Mathematics in the Sciences in Leipzig. In contrast to usual proceeding volumes, instead of reporting on the most recent technical results, contributors were asked to discuss visions and new ideas in foundational physics, in particular concerning foundations of quantum field theory. A special focus has been put on the question of which physical principles of quantum (field) theory can be considered fundamental in view of gravity. The book is mainly addressed to mathematicians and physicists who are interested in fundamental questions of mathematical physics. It allows the reader to obtain a broad and up-to-date overview of a fascinating active research area.

This volume offers a selection of the best contributions by Russian scholars--historians and philosophers of science--to the Einstein Studies industry, broadly construed. Most of the papers included here were first published in Russian in the 'Einshteinovskiy Sbornik' series (Einstein Studies), the first of its kind, and initiated in 1966 by Nobel Prize winner Igor Tamm. From 1966-1990, fourteen volumes of the 'Sbornik' were published by Nauka, the chief academic publisher in the former Soviet Union. The book explores such topics as the historical and foundational issues in general relativity and relativistic cosmology, Einstein's contributions to quantum theory of radiation, and the rise of Dirac's quantum electrodynamics. The volume also includes a detailed description of the physics colloquium Einstein established and coordinated in 1912-1914 in Zurich. The contributors draw extensively on documentation previously unavailable to most scholars. Thus the materials from various Russian archives shed new light on the famous exchange (regarding the first evolutionary cosmological models) between Einstein and Aleksandr Friedmann in the early 1920s and on the role of Boris Podolsky and Vladimir Fock in the emergence of quantum electrodynamics. The little- known correspondence between Einstein and a famous German pilot Paul Ehrhardt suggests that, during World War I, Einstein was involved with aero- and hydrodynamics and thought about ways of improving airfoil design. Other articles discuss new approaches to important questions in the foundations of general relativity and cosmology. Historians, philosophers, and sociologists of science should be prepared to find much new and unexpected material in this engaging volume presenting the best of the recent Russian scholarship in the field. The book will be accessible to the general reader as well.

Building from foundations of modern science and cosmic evolution, as well as psychological and philosophical perspectives of value and meaning, this book explores some of humanity's biggest questions: * Is the Universe "about something"? * What might be roles for life and intelligence in cosmic evolution? * How might we think about value, meaning, purpose, and ethics in a cosmic evolutionary context? The author explores how the sciences of relativity and quantum theory, combined with cosmic evolution and philosophical traditions such as process philosophy, contribute to the development of a broad "relationalist framework". That framework helps inform perspectives such as "scientific minimalism" and "cosmological theories of value". Cosmological Reverence, Cosmocultural Evolution, and the Connection-Action Principle are explored as examples of cosmological theories of value, all of which help inform how we might think about ethics, value, and meaning in a cosmic context - including application to the search for extraterrestrial life and the future of intelligence in the universe. This book will benefit a diverse range of practitioners in philosophy, science, and policy, including interdisciplinary fields such as Science and Society and cultural evolution studies. From the Foreword: "This volume ranges from the sciences of cosmic evolution, relativity, and quantum mechanics, to value theory and process philosophy, all with the goal of exploring how they relate to humanity in the sense of worldviews and meaning. With his three cosmological theories of value, Lupisella goes beyond the bounds of most books on naturalism, and into fundamental questions about the nature of the universe and our relation to it. To read Lupisella is to have a mind-boggling experience, to want to race to references, to want to know more." Steven J. Dick Former Baruch S. Blumberg NASA/ Library of Congress Chair in Astrobiology Former NASA Chief Historian

The book expounds the major topics in the special theory of relativity. It provides a detailed examination of the mathematical foundation of the special theory of relativity, relativistic mass, relativistic mechanics and relativistic electrodynamics. As well as covariant formulation of relativistic mechanics and electrodynamics, the book discusses the relativistic effect on photons. Using a mathematical approach, the text offers graduate students a clear, concise view of the special theory of relativity. Organized into 14 chapters and two appendices, the content is presented in a logical order, and every topic has been dealt with in a simple and lucid manner. To aid understanding of the subject, the book provides numerous relevant worked examples in every chapter. The book's mathematical approach helps students in their independent study and motivates them to research the topic further.

This Ph.D. thesis is a search for physics beyond the standard model (SM) of particle physics, which successfully describes the interactions and properties of all known elementary particles. However, no particle exists in the SM that can account for the dark matter, which makes up about one quarter of the energy-mass content of the universe. Understanding the nature of dark matter is one goal of the CERN Large Hadron Collider (LHC). The extension of the SM with supersymmetry (SUSY) is considered a promising possibilities to explain dark matter. The nominated thesis describes a search for SUSY using data collected by the CMS experiment at the LHC. It utilizes a final state consisting of a photon, a lepton, and a large momentum imbalance probing a class of SUSY models that has not yet been studied extensively. The thesis stands out not only due to its content that is explained with clarity but also because the author performed more or less all aspects of the thesis analysis by himself, from data skimming to limit calculations, which is extremely rare, especially nowadays in the large LHC collaborations.