The aim of this book is to give graduate students an overview of quantum gravity but it also covers related topics from astrophysics. Some well-written contributions can serve as an introduction into basic conceptual concepts like time in quantum gravity or the emergence of a classical world from quantum cosmology. This makes the volume attractive to philosophers of science, too. Other topics are black holes, gravitational waves and non-commutative extensions of physical theories.

Quantum optics, i.e. the interaction of individual photons with matter, began with the discoveries of Planck and Einstein, but in recent years, it has expanded beyond pure physics to become an important driving force for technological innovation. This book serves the broader readership growing out of this development by starting with an elementary description of the underlying physics and then building up a more advanced treatment. The reader is led from the quantum theory of the simple harmonic oscillator to the application of entangled states to quantum information processing.
An equally important feature of the text is a strong emphasis on experimental methods. Primary photon detection, heterodyne and homodyne techniques, spontaneous down-conversion, and quantum tomography are discussed, together with important experiments. These experimental and theoretical considerations come together in the chapters describing quantum cryptography, quantum communications, and quantum computing.

Beautifully illustrated and engagingly written, Twelve Lectures in Quantum Mechanics presents theoretical physics with a breathtaking array of examples and anecdotes. Basdevant's style is clear and stimulating, in the manner of a brisk lecture that can be followed with ease and enjoyment. Here is a sample of the book's style, from the opening of Chapter 1: "If one were to ask a passer-by to quote a great formula of physics, chances are that the answer would be 'E = mc2'.... There is no way around it: all physics is quantum, from elementary particles, to stellar physics and the Big Bang, not to mention semiconductors and solar cells."

This book investigates two possibilities for describing classical-mechanical physical systems along with their Hamiltonian dynamics in the framework of quantum mechanics.The first possibility consists in exploiting the geometrical properties of the set of quantum pure states of "microsystems" and of the Lie groups characterizing the specific classical system. The second approach is to consider quantal systems of a large number of interacting subsystems - i.e. macrosystems, so as to study the quantum mechanics of an infinite number of degrees of freedom and to look for the behaviour of their collective variables. The final chapter contains some solvable models of "quantum measurement" describing dynamical transitions from "microsystems" to "macrosystems".

But to admit things not visible to the gross creatures that we are is, in my opinion, to show a decent humility, and not just a lamentable addiction to metaphysics. J. S. Bell, Are There Quantum Jumps? ON CANADIAN THANKSGIVING WEEKEND in the autumn of 1994, a lively conference was held at The University of Western Ontario under the title "Conceptual Problems of Relativistic Quantum Mechanics." Most of the eighteen papers in this volume are directly connected with that conference. Articles by both theoretical physicists and philosophers of science are included, and many authors will be recognized immediately for their already substantive work in the foundations of physics. A quarter century ago Howard Stein suggested that relativistic quantum field theory should be 'the contemporary locus of metaphysical research', but there were few takers. Only fairly recently has that changed, with the result that the bulk of the papers here pursue issues that go beyond nonrelativistic quantum mechanics (or at least have serious implications for its relativistic generalization). Nevertheless, problems interpreting the nonrelativistic theory remain a persistent thorn in the side of any such endeavor, and so some of the papers develop innovative approaches to those issues as well.

The book is based on the author's PhD thesis, which deals with the concept of time in quantum gravity and its relevance for the physics of the early Universe. It presents a consistent and complete new relational formulation of quantum gravity (more specifically, of quantum mechanics models with diffeomorphism invariance), which is applied to potentially observable cosmological effects. The work provides answers to the following questions: How can the dynamics of quantum states of matter and geometry be defined in a diffeomorphism-invariant way? What is the relevant space of physical states and which operators act on it? How are the quantum states related to probabilities in the absence of a preferred time? The answers can provide a further part of the route to constructing a fundamental theory of quantum gravity. The book is well-suited to graduate students as well as professional researchers in the fields of general relativity and gravitation, cosmology, and quantum foundations.

This thesis studies various aspects of non-critical strings both as an example of a non-trivial and solvable model of quantum gravity and as a consistent approximation to the confining flux tube in quantum chromodynamics (QCD). It proposes and develops a new technique for calculating the finite volume spectrum of confining flux tubes. This technique is based on approximate integrability and it played a game-changing role in the study of confining strings. Previously, a theoretical interpretation of available high quality lattice data was impossible, because the conventional perturbative expansion for calculating the string spectra was badly asymptotically diverging in the regime accessible on the lattice. With the new approach, energy levels can be calculated for much shorter flux tubes than was previously possible, allowing for a quantitative comparison with existing lattice data. The improved theoretical control makes it manifest that existing lattice data provides strong evidence for a new pseudoscalar particle localized on the QCD fluxtube - the worldsheet axion. The new technique paves a novel and promising path towards understanding the dynamics of quark confinement.

This edited collection provides new perspectives on some metaphysical questions arising in quantum mechanics. These questions have been long-standing and are of continued interest to researchers and graduate students working in physics, philosophy of physics, and metaphysics. It features contributions from a diverse set of researchers, ranging from senior scholars to junior academics, working in varied fields, from physics to philosophy of physics and metaphysics. The contributors reflect on issues about fundamentality (is quantum theory fundamental? If so, what is its fundamental ontology?), ontological dependence (how do ordinary objects exist even if they are not fundamental?), realism (what kind of realism is compatible with quantum theory?), indeterminacy (can the world itself exhibit ontological indeterminacy?). The book contains contributions from both physicists (including Nobel Prize winner Gerard 't Hooft), science communicators and philosophers.

This work presents some essential techniques that constitute the modern strategy for computing scattering amplitudes. It begins with an introductory chapter to fill the gap between a standard QFT course and the latest developments in the field. The author then tackles the main bottleneck: the computation of the loop Feynman integrals. The most efficient technique for their computation is the method of the differential equations. This is discussed in detail, with a particular focus on the mathematical aspects involved in the derivation of the differential equations and their solution. Ample space is devoted to the special functions arising from the differential equations, to their analytic properties, and to the mathematical techniques which allow us to handle them systematically. The thesis also addresses the application of these techniques to a cutting-edge problem of importance for the physics programme of the Large Hadron Collider: five-particle amplitudes at two-loop order. It presents the first analytic results for complete two-loop five-particle amplitudes, in supersymmetric theories and QCD. The techniques discussed here open the door to precision phenomenology for processes of phenomenological interest, such as three-photon, three-jet, and di-photon + jet production.

This book focuses on unstable systems both from the classical and the quantum mechanical points of view and studies the relations between them. The first part deals with quantum systems. Here the main generally used methods today, such as the Gamow approach, and the Wigner-Weisskopf method, are critically discussed. The quantum mechanical Lax-Phillips theory developed by the authors, based on the dilation theory of Nagy and Foias and its more general extension to approximate semigroup evolution is explained. The second part provides a description of approaches to classical stability analysis and introduces geometrical methods recently developed by the authors, which are shown to be highly effective in diagnosing instability and, in many cases, chaotic behavior. It is then shown that, in the framework of the theory of symplectic manifolds, there is a systematic algorithm for the construction of a canonical transformation of any standard potential model Hamiltonian to geometric form, making accessible powerful geometric methods for stability analysis in a wide range of applications.

After an extensive overview of the Standard Model and of the theory and phenomenology of Supersymmetry, this book describes the recent development of the ATLAS Particle Flow algorithm, a hadronic reconstruction technique aiming at enhancing the sensitivity of the experiment to new physics through the combination of the information from different ATLAS sub-detectors. The first ever ATLAS strong SUSY search exploiting this technique is also described, reporting the results and exclusion limits obtained using the complete proton-proton collision dataset recorded by the ATLAS experiment during the second Run of the Large Hadron Collider (LHC).

This book offers a rigorous yet elementary approach to quantum mechanics that will meet the needs of Master's-level Mathematics students and is equally suitable for Physics students who are interested in gaining a deeper understanding of the mathematical structure of the theory. Throughout the coverage, which is limited to single-particle quantum mechanics, the focus is on formulating theory and developing applications in a mathematically precise manner. Following a review of selected key concepts in classical physics and the historical background, the basic elements of the theory of operators in Hilbert spaces are presented and used to formulate the rules of quantum mechanics. The discussion then turns to free particles, harmonic oscillators, delta potential, and hydrogen atoms, providing rigorous proofs of the corresponding dynamical properties. Starting from an analysis of these applications, readers are subsequently introduced to more advanced topics such as the classical limit, scattering theory, and spectral analysis of Schroedinger operators. The main content is complemented by numerous exercises that stimulate interactive learning and help readers check their progress.

This thesis presents several related advances in the field of nonequilibrium quantum thermodynamics. The central result is an ingenious proof that the local temperature and voltage measurement in a nonequilibrium system of fermions exists and is unique, placing the concept of local temperature on a rigorous mathematical footing for the first time. As an intermediate step, a proof of the positivity of the Onsager matrix of linear response theory is given -- a statement of the second law of thermodynamics that had lacked an independent proof for 85 years. A new experimental method to measure the local temperature of an electron system using purely electrical techniques is also proposed, which could enable improvements to the spatial resolution of thermometry by several orders of magnitude. Finally, a new mathematically-exact definition for the local entropy of a quantum system in a nonequilibrium steady state is derived. Several different measures of the local entropy are discussed, relating to the thermodynamics of processes that a local observer with varying degrees of information about the microstates of the system could carry out, and it is shown that they satisfy a hierarchy of inequalities. Proofs of the third law of thermodynamics for generic open quantum systems are presented, taking into account the entropic contribution due to localized states. Appropriately normalized (per-state) local entropies are defined and are used to quantify the departure from local equilibrium.

The Industrial Revolution meets the quantum-technology revolution! A steampunk adventure guide to how mind-blowing quantum physics is transforming our understanding of information and energy. Victorian era steam engines and particle physics may seem worlds (as well as centuries) apart, yet a new branch of science, quantum thermodynamics, reenvisions the scientific underpinnings of the Industrial Revolution through the lens of today's roaring quantum information revolution. Classical thermodynamics, understood as the study of engines, energy, and efficiency, needs reimagining to take advantage of quantum mechanics, the basic framework that explores the nature of reality by peering at minute matters, down to the momentum of a single particle. In her exciting new book, intrepid Harvard-trained physicist Dr. Nicole Yunger Halpern introduces these concepts to the uninitiated with what she calls "quantum steampunk," after the fantastical genre that pairs futuristic technologies with Victorian sensibilities. While readers follow the adventures of a rag-tag steampunk crew on trains, dirigibles, and automobiles, they explore questions such as, "Can quantum physics revolutionize engines?" and "What deeper secrets can quantum information reveal about the trajectory of time?" Yunger Halpern also describes her own adventures in the quantum universe and provides an insider's look at the work of the scientists obsessed with its technological promise. Moving from fundamental physics to cutting-edge experimental applications, Quantum Steampunk explores the field's aesthetic, shares its whimsy, and gazes into the potential of a quantum future. The result is a blast for fans of science, science fiction, and fantasy.

Superfluid helium is a quantum liquid that exhibits a range of counter-intuitive phenomena such as frictionless flow. Quantized vortices are a particularly important feature of superfluid helium, and all superfluids, characterized by a circulation that can only take prescribed integer values. However, the strong interactions between atoms in superfluid helium prohibit quantitative theory of vortex behaviour. Experiments have similarly not been able to observe coherent vortex dynamics. This thesis resolves this challenge, bringing microphotonic techniques to bear on two-dimensional superfluid helium, observing coherent vortex dynamics for the first time, and achieving this on a silicon chip. This represents a major scientific contribution, as it opens the door not only to providing a better understanding of this esoteric quantum state of matter, but also to building new quantum technologies based upon it, and to understanding the dynamics of astrophysical superfluids such as those thought to exist in the core of neutron stars.

This book presents a basic introduction to quantum mechanics. Depending on the choice of topics, it can be used for a one-semester or two-semester course. An attempt has been made to anticipate the conceptual problems students encounter when they first study quantum mechanics. Wherever possible, examples are given to illustrate the underlying physics associated with the mathematical equations of quantum mechanics. To this end, connections are made with corresponding phenomena in classical mechanics and electromagnetism. The problems at the end of each chapter are intended to help students master the course material and to explore more advanced topics. Many calculations exploit the extraordinary capabilities of computer programs such as Mathematica, MatLab, and Maple. Students are urged to use these programs, just as they had been urged to use calculators in the past. The treatment of various topics is rather complete, in that most steps in derivations are included. Several of the chapters go beyond what is traditionally covered in an introductory course. The goal of the presentation is to provide the students with a solid background in quantum mechanics.

This book introduces the reader to the field of jet substructure, starting from the basic considerations for capturing decays of boosted particles in individual jets, to explaining state-of-the-art techniques. Jet substructure methods have become ubiquitous in data analyses at the LHC, with diverse applications stemming from the abundance of jets in proton-proton collisions, the presence of pileup and multiple interactions, and the need to reconstruct and identify decays of highly-Lorentz boosted particles. The last decade has seen a vast increase in our knowledge of all aspects of the field, with a proliferation of new jet substructure algorithms, calculations and measurements which are presented in this book. Recent developments and algorithms are described and put into the larger experimental context. Their usefulness and application are shown in many demonstrative examples and the phenomenological and experimental effects influencing their performance are discussed. A comprehensive overview is given of measurements and searches for new phenomena performed by the ATLAS and CMS Collaborations. This book shows the impressive versatility of jet substructure methods at the LHC.

A gentle introduction to the physics of quantized fields and many-body physics. Based on courses taught at the University of Illinois, it concentrates on the basic conceptual issues that many students find difficult, and emphasizes the physical and visualizable aspects of the subject. While the text is intended for students with a wide range of interests, many of the examples are drawn from condensed matter physics because of the tangible character of such systems. The first part of the book uses the Hamiltonian operator language of traditional quantum mechanics to treat simple field theories and related topics, while the Feynman path integral is introduced in the second half where it is seen as indispensable for understanding the connection between renormalization and critical as well as non-perturbative phenomena.

The lecture notes of Julian Schwinger's UCLA course consist of three parts corresponding to the three quarters of teaching. The first part begins with an analysis of Stern--Gerlach-type experiments which accomplishes a self-contained physical and mathematical development of the general structure of quantum kinematics. The second part proceeds from there. The response to infinitesimal time displacements yields the equations of motion. Then the Quantum Action Principle (QAP) is derived, and accepted as a fundamental principle. In a sense, the rest of part two and all of part three consist of instructive applications of the QAP.

This thesis summarizes the original analysis work performed by the author on data from XENON1T, a search for dark matter with a ton-size noble liquid detector operated at Gran Sasso Underground Laboratory in Italy. The nature of dark matter is one of the most open and pressing questions of modern physics, and the unique data acquired with this detector allows the exploration and investigation of several potential scenarios. The analysis of Dr. Shockley searches for a class of elusive elementary particles that interact with the electrons of ordinary atoms, instead of the nucleus. Results of the analysis present, with high confidence, an excess with respect to the expected background. Beyond more mundane explanations, this additional rate of electron-mediated interactions might be a first hint of physics beyond the standard model. This accessible thesis provides details on the detector, the data, and the theory, delivering to the reader an in-depth and coherent picture of the search for physics beyond the standard model.

It is hard to interpret quantum mechanics. The most surprising, but also most parsimonious, interpretation is the many-worlds, or quantum-multiverse interpretation, implying a permanent coexistence of parallel realities. Could this perhaps be the appropriate interpretation of quantum mechanics? This book collects evidence for this interpretation, both from physics and from other fields, and proposes a subjectivist version of it, the clustered-minds multiverse. The author explores its implications through the lens of decision making and derives consequences for free will and consciousness. For example, free will can be implemented in the form of vectorial choices, as introduced in the book. He furthermore derives consequences for research in the social sciences, especially in psychology and economics.

This book presents more than 300 exercises, with guided solutions, on topics that span both the experimental and the theoretical aspects of particle physics. The exercises are organized by subject, covering kinematics, interactions of particles with matter, particle detectors, hadrons and resonances, electroweak interactions and flavor physics, statistics and data analysis, and accelerators and beam dynamics. Some 200 of the exercises, including 50 in multiple-choice format, derive from exams set by the Italian National Institute for Nuclear Research (INFN) over the past decade to select its scientific staff of experimental researchers. The remainder comprise problems taken from the undergraduate classes at ETH Zurich or inspired by classic textbooks. Whenever appropriate, in-depth information is provided on the source of the problem, and readers will also benefit from the inclusion of bibliographic details and short dissertations on particular topics. This book is an ideal complement to textbooks on experimental and theoretical particle physics and will enable students to evaluate their knowledge and preparedness for exams.

In this volume we have collected some of the contributions made to the Twelfth European Workshop on Quantum Systems in Chemistry and Physics (QSCP-XII) in 2007. The workshop was held at Royal Holloway College, the most westerly campusof the University of London,and situated just a stone's throw from Windsor Great Park. The workshop, which ran from 30 August to 5 September, continued the series that was established by Roy McWeeny in April 1996 with a meeting held at San Miniato, near Pisa. The purpose of the QSCP workshops is to bring together, in an informal atmosphere and with the aim of fostering collaboration, those chemists and physicists who share a common ?eld of interest in the theory of the quantum many-body problem. Quantum mechanics provides a theoretical foundation for our understandingof the structure,propertiesanddynamicsof atoms, moleculesandthe solid state, in terms of their component particles: electrons and nuclei. The study of 'Quantum Systems in Chemistry and Physics' therefore underpins many of the emerging?elds in twenty-?rstcenturyscience andtechnology:nanostructure,smart materials, drug design - to name but a few. Members of the workshop were keen to discuss their research and engage in collaboration centred upon the development of fundamental and innovative theory which would lead to the exploration of new concepts. The proceedings of all of the workshops, which have been held annually since 1996, have been published both to disseminate the latest developments within the wider community and to stimulate further collaboration.

In each generation, scientists must redefine their fields: abstracting, simplifying and distilling the previous standard topics to make room for new advances and methods. Sethna's book takes this step for statistical mechanics--a field rooted in physics and chemistry whose ideas and methods< br> are now central to information theory, complexity, and modern biology. Aimed at advanced undergraduates and early graduate students in all of these fields, Sethna limits his main presentation to the topics that future mathematicians and biologists, as well as physicists and chemists, will find< br> fascinating and central to their work. The amazing breadth of the field is reflected in the author's large supply of carefully crafted exercises, each an introduction to a whole field of study: everything from chaos through information theory to life at the end of the universe.

This volume contains contributions based on the lectures delivered and posters presented at the Fifth International Conference on Quantum Communication, Measurement and Computing (QCM&C-Y2K). This Conference is the fifth of a successful series hosted this time in Italy, was held in Capri, 3-7 July, 2000. The conference was attended by more than 200 participants from all over the world. There was also a high level of participation from graduate students, who greatly benefited from the opportunity to attend world-class conferences. The Conference Hall was hosted in La Residenza Hotel in Capri, where part of p- ticipants where housed, while others where housed in various cozy nearby - tels. All enjoyed the pleasant atmosphere offered by the island of Capri. There were 59 invited lectures given as oral presentations of 30 minutes and 94 poster papers. The major topics covered at the Conference where new experimental and theoretical results in quantum information. They were divided in five parts; i) Quantum Information and Communication, ii) Quantum Measurement, - coherence, and Tomography, iii) Quantum Computing, iv) Cryptography, v) Entanglement and Teleportation. We were lucky in that almost all major - perimental groups in the world working in this area were represented, as were the major theoreticians. There was very active audience participation. A n- ber of graduate students and post-docs were able to present their contributions in four after dinner poster sessions.