This fourth edition of selecta of my work on the stability of matter contains recent work on two topics that continue to fascinate me: Quantum electrodynamics (QED) and the Bose gas. Three papers have been added to Part VII on QED. As I mentioned in the preface to the third edition, there must be a way to formulate a non-perturbative QED, presumably with an ultraviolet cutoff, that correctly describes low energy physics, i.e., ordinary matter and its interaction with the electromagnetic field. The new paper VII.5, which quantizes the results in V.9, shows that the elementary no-pair version of relativistic QED (using the Dirac operator) is unstable when many-body effects are taken into account. Stability can be restored, however, if the Dirac operator with the field, instead of the bare Dirac operator, is used to define an electron. Thus, the notion of a bare electron without its self-field is physically questionable."

This book and its sequel (Theories of Matter Space and Time: Quantum Theories) are taken from third and fourth year undergraduate Physics courses at Southampton University, UK. The aim of both books is to move beyond the initial courses in classical mechanics, special relativity, electromagnetism, and quantum theory to more sophisticated views of these subjects and their interdependence. The goal is to guide undergraduates through some of the trickier areas of theoretical physics with concise analysis while revealing the key elegance of each subject. The first chapter introduces the key areas of the principle of least action, an alternative treatment of Newtownian dynamics, that provides new understanding of conservation laws. In particular, it shows how the formalism evolved from Fermat's principle of least time in optics. The second introduces special relativity leading quickly to the need and form of four-vectors. It develops four-vectors for all kinematic variables and generalize Newton's second law to the relativistic environment; then returns to the principle of least action for a free relativistic particle. The third chapter presents a review of the integral and differential forms of Maxwell's equations before massaging them to four-vector form so that the Lorentz boost properties of electric and magnetic fields are transparent. Again, it then returns to the action principle to formulate minimal substitution for an electrically charged particle.

This textbook on Feynman integrals starts from the basics, requiring only knowledge of special relativity and undergraduate mathematics. Feynman integrals are indispensable for precision calculations in quantum field theory. At the same time, they are also fascinating from a mathematical point of view. Topics from quantum field theory and advanced mathematics are introduced as needed. The book covers modern developments in the field of Feynman integrals. Topics included are: representations of Feynman integrals, integration-by-parts, differential equations, intersection theory, multiple polylogarithms, Gelfand-Kapranov-Zelevinsky systems, coactions and symbols, cluster algebras, elliptic Feynman integrals, and motives associated with Feynman integrals. This volume is aimed at a) students at the master's level in physics or mathematics, b) physicists who want to learn how to calculate Feynman integrals (for whom state-of-the-art techniques and computations are provided), and c) mathematicians who are interested in the mathematical aspects underlying Feynman integrals. It is, indeed, the interwoven nature of their physical and mathematical aspects that make Feynman integrals so enthralling.

This is a new volume of original essays on the metaphysics of quantum mechanics. The essays address questions such as: What fundamental metaphysics is best motivated by quantum mechanics? What is the ontological status of the wave function? Does quantum mechanics support the existence of any other fundamental entities, e.g. particles? What is the nature of the fundamental space (or space-time manifold) of quantum mechanics? What is the relationship between the fundamental ontology of quantum mechanics and ordinary, macroscopic objects like tables, chairs, and persons? The volume includes a comprehensive introduction with a history of quantum mechanics and the debate over its metaphysical interpretation focusing especially on the main realist alternatives.

In 1964, a mechanism explaining the origin of particle masses was proposed by Robert Brout, Francois Englert, and Peter W. Higgs. 48 years later, in 2012, the so-called Higgs boson was discovered in proton-proton collisions recorded by experiments at the LHC. Since then, its ability to interact with quarks remained experimentally unconfirmed. This book presents a search for Higgs bosons produced in association with top quarks tt H in data recorded with the CMS detector in 2016. It focuses on Higgs boson decays into bottom quarks H bb and top quark pair decays involving at least one lepton. In this analysis, a multiclass classification approach using deep learning techniques was applied for the first time. In light of the dominant background contribution from tt production, the developed method proved to achieve superior sensitivity with respect to existing techniques. In combination with searches in different decay channels, the presented work contributed to the first observations of tt H production and H bb decays.

The ancient Greeks believed that everything in the Universe should be describable in terms of geometry. This thesis takes several steps towards realising this goal by introducing geometric descriptions of systems such as quantum gravity, fermionic particles and the origins of the Universe itself. The author extends the applicability of previous work by Vilkovisky, DeWitt and others to include theories with spin 1/2 and spin 2 degrees of freedom. In addition, he introduces a geometric description of the potential term in a quantum field theory through a process known as the Eisenhart lift. Finally, the methods are applied to the theory of inflation, where they show how geometry can help answer a long-standing question about the initial conditions of the Universe. This publication is aimed at graduate and advanced undergraduate students and provides a pedagogical introduction to the exciting topic of field space covariance and the complete geometrization of quantum field theory.

Using a selection of key experiments performed over the past 30 years or so, we present a discussion of the strikingly counter-intuitive phenomena of the quantum world that defy explanation in terms of everyday "common sense" reasoning, and we provide the corresponding quantum mechanical explanations with a very elementary use of associated formalism. Most, but certainly not all, of the experiments we describe are optical experiments involving a very small number of photons (particles of light). We begin with experiments on the wave-particle duality of electrons, proceed to experiments on the particle nature of light and single photon interference, delayed choice experiments and interaction-free detection, then go on to experiments involving the interference of two photons, quantum entanglement and Bell's Theorem, quantum teleportation, large-scale quantum effects and the divide between the classical and quantum worlds, addressing the question as to whether or not there is such a divide.

Flavor physics is fundamental to test the Standard Model of particle physics and could be the key to discover new physics. This book explores lepton flavor violating implications in the low scale seesaw models, a well-motivated scenario for explaining the still open problem of neutrino mass generation. It studies the lepton flavor violating Higgs decays in depth, developing useful simple expressions for making fast estimations of this observable. It also introduces a new parametrization optimized for the study of lepton flavor violation in these models, showing that high rates could be obtained for Higgs and Z decays if these new heavy neutrinos have masses in the TeV range. Lastly, it goes on to explore the possibility of their production and decay at the Large Hadron Collider through events with two charged leptons of different flavor.

With a minimum of mathematics, this book provides a novel approach to the teaching of quantum mechanics. As many books mainly present the concepts of quantum theory, this volume emphasises the application of the theory, offering the reader a unifying picture of atoms, molecules and solids. Essential for all undergraduate physics courses, it will also be a most valuable supplementary text for postgraduate courses on quantum mechanics.

This book provides an overview of state-of-the-art implementations of quantum random number generators (QRNGs), and especially examines their relation to classical statistical randomness models and numerical techniques for computing random numbers. The reader - who ideally has a background in classical statistics, computer science, or cryptography - is introduced to the world of quantum bits step by step, and explicit relations between QRNGs and their classical counterparts are identified along the way. Random number generation is a major pillar of cryptography. Capitalizing on the randomness inherent in quantum phenomena is a rapidly evolving branch of quantum cryptography with countless applications for the future. The value of quantum randomness for cryptographic purposes is empirically demonstrated in statistical evaluations of QRNGs' performance compared to classical techniques for true and pseudorandom number generation. The book then provides an overview of technical implementations of QRNGs, before a concluding discussion of major achievements and remaining obstacles in the field rounds out the coverage, while also opening the door for future research directions.

Over the years enormous effort was invested in proving ergodicity, but for a number of reasons, con?dence in the fruitfulness of this approach has waned. - Y. Ben-Menahem and I. Pitowsky [1] Abstract The basic motivation behind the present text is threefold: To give a new explanation for the emergence of thermodynamics, to investigate the interplay between quantum mechanics and thermodynamics, and to explore possible ext- sions of the common validity range of thermodynamics. Originally, thermodynamics has been a purely phenomenological science. Early s- entists (Galileo, Santorio, Celsius, Fahrenheit) tried to give de?nitions for quantities which were intuitively obvious to the observer, like pressure or temperature, and studied their interconnections. The idea that these phenomena might be linked to other ?elds of physics, like classical mechanics, e.g., was not common in those days. Such a connection was basically introduced when Joule calculated the heat equ- alent in 1840 showing that heat was a form of energy, just like kinetic or potential energy in the theory of mechanics. At the end of the 19th century, when the atomic theory became popular, researchers began to think of a gas as a huge amount of bouncing balls inside a box.

This thesis focuses on searches for squarks with the ATLAS detector in "compressed" scenarios where the scalar top is very close in mass to the lightest supersymmetric particle. These models are theoretically appealing because the presence of a quasi-degenerate scalar top enhances the self-annihilation cross-section of the lightest supersymmetric particle, acting therefore as a regulator of the dark matter relic density. Two main analyses are presented: the first is a search for scalar tops decaying to charm quarks. The identification of jets originating from the charm quark is very challenging due to its short lifetime. The calibration of tools for charm-tagging has paved the way to measuring the decay of the Higgs boson to pairs of charm quarks. The second analysis presented is the development of a novel technique for reconstructing low momentum b-hadrons. This tool has enabled the ATLAS collaboration to explore topologies that were previously inaccessible.

Effects of many-body interactions and superconducting correlations have become central questions in the quantum transport community. While most previous works investigating current fluctuations in nanodevices have been restricted to the stationary regime, Seoane's thesis extends these studies to the time domain. It provides relevant information about the time onset of electronic correlations mediated by interactions and superconductivity. This knowledge is essential for the development of fast electronic devices, as well as novel applications requiring fast manipulations, such as quantum information processing. In addition, the thesis establishes contact with issues of broad current interest such as non-equilibrium quantum phase transitions.

This book includes topics in nanophysics, nanotechnology, nanomaterials, sensors, biosensors, security systems, and CBRN agents detection. There have been many significant advances in the past two years and some entirely new directions of research are just opening up. Recent developments in nanotechnology and measurement techniques now allow experimental investigation of the physical properties of nanostructured materials. The book presents new methods for the detection of chemical, biological, radiological and nuclear (CBRN) agents using chemical and biochemical sensors. Identification, protection and decontamination are the main scientific and technological responses for the modern challenges of CBRN agents.

The wealth of recent cosmic microwave background and large-scale structure data has transformed the field of cosmology. These observations have not only become precise enough to answer questions about the universe on the largest scales, but also to address puzzles in the microscopic description of Nature. This thesis investigates new ways of probing the early universe, the properties of neutrinos and the possible existence of other light particles. In particular, based on detailed theoretical insights and novel analyses, new evidence for the cosmic neutrino background is found in the distribution of galaxies and in cosmic microwave background data. This tests the Standard Model of particle physics and the universe back to a time when it was about one second old. Furthermore, it is demonstrated that future observations will be capable of probing physics beyond the Standard Model since they can achieve a particular target which would either allow the detection of any light particles that have ever been in thermal equilibrium or imply strong bounds on their properties.

This thesis shows how a combination of analytic and numerical techniques, such as a time dependent and finite temperature Density Matrix Renormalization Group (DMRG) technique, can be used to obtain the physical properties of low dimensional quantum magnets with an unprecedented level of accuracy. A comparison between the theory and experiment then enables these systems to be used as quantum simulators; for example, to test various generic properties of low dimensional systems such as Luttinger liquid physics, the paradigm of one dimensional interacting quantum systems. Application of these techniques to a material made of weakly coupled ladders (BPCB) allowed the first quantitative test of Luttinger liquids. In addition, other physical quantities (magnetization, specific heat etc.), and more remarkably the spins-spin correlations - directly measurable in neutron scattering experiments - were in excellent agreement with the observed quantities. We thus now have tools to quantitatiively assess the dynamics for this class of quantum systems.

From the Royal Society Winton Prize winner 'Sean Carroll examines what it means to exist on this speck of dust in a possibly infinite universe. It's fascinating to see a real working physicist thinking these things through and trying to come to a conclusion.' - Professor Brian Cox on The Big Picture, a Mail on Sunday Book of the Year Quantum physics is not mystifying. The implications are mind-bending, and not yet fully understood, but this revolutionary theory is truly illuminating. It stands as the best explanation of the fundamental nature of our world. Spanning the history of quantum discoveries, from Einstein and Bohr to the present day, Something Deeply Hidden is the essential guide to the most intriguing subject in science. Acclaimed physicist and writer Sean Carroll debunks the myths, resurrects and reinstates the Many-Worlds interpretation, and presents a new path towards solving the apparent conflict between quantum mechanics and Einstein's theory of general relativity. In doing so, he fills a gap in the science that has existed for almost a century. A magisterial tour, Something Deeply Hidden encompasses the cosmological and everyday implications of quantum reality and multiple universes. And - finally - it all makes sense.

Classical Mechanics teaches readers how to solve physics problems; in other words, how to put math and physics together to obtain a numerical or algebraic result and then interpret these results physically. These skills are important and will be needed in more advanced science and engineering courses. However, more important than developing problem-solving skills and physical-interpretation skills, the main purpose of this multi-volume series is to survey the basic concepts of classical mechanics and to provide the reader with a solid understanding of the foundational content knowledge of classical mechanics. Classical Mechanics: Tools and Vectors is simply about transmitting information. The conventions used to transmit certain types of numerical information are crucial concepts that must be addressed at the outset of any series on classical mechanics by discussing scalars versus vectors for example.

This book presents a comprehensive overview of state-of-the-art quantum dot photodetectors, including device fabrication technologies, optical engineering/manipulation strategies, and emerging photodetectors with building blocks of novel quantum dots (e.g. perovskite) as well as their hybrid structured (e.g. 0D/2D) materials. Semiconductor quantum dots have attracted much attention due to their unique quantum confinement effect, which allows for the facile tuning of optical properties that are promising for next-generation optoelectronic applications. Among these remarkable properties are large absorption coefficient, high photosensitivity, and tunable optical spectrum from ultraviolet/visible to infrared region, all of which are very attractive and favorable for photodetection applications. The book covers both fundamental and frontier research in order to stimulate readers' interests in developing novel ideas for semiconductor photodetectors at the center of future developments in materials science, nanofabrication technology and device commercialization. The book provides a knowledge sharing platform and can be used as a reference for researchers working in the fields of photonics, materials science, and nanodevices.

This volume of the CRM Conference Series is based on a carefully refereed selection of contributions presented at the "11th International Symposium on Quantum Theory and Symmetries", held in Montreal, Canada from July 1-5, 2019. The main objective of the meeting was to share and make accessible new research and recent results in several branches of Theoretical and Mathematical Physics, including Algebraic Methods, Condensed Matter Physics, Cosmology and Gravitation, Integrability, Non-perturbative Quantum Field Theory, Particle Physics, Quantum Computing and Quantum Information Theory, and String/ADS-CFT. There was also a special session in honour of Decio Levi. The volume is divided into sections corresponding to the sessions held during the symposium, allowing the reader to appreciate both the homogeneity and the diversity of mathematical tools that have been applied in these subject areas. Several of the plenary speakers, who are internationally recognized experts in their fields, have contributed reviews of the main topics to complement the original contributions.

The scattering theory for transport phenomena was initiated by P. Lax and R. Phillips in 1967. Since then, great progress has been made in the field and the work has been ongoing for more than half a century. This book shows part of that progress. The book is divided into 7 chapters, the first of which deals with preliminaries of the theory of semigroups and C*-algebra, different types of semigroups, Schatten-von Neuman classes of operators, and facts about ultraweak operator topology, with examples using wavelet theory. Chapter 2 goes into abstract scattering theory in a general Banach space. The wave and scattering operators and their basic properties are defined. Some abstract methods such as smooth perturbation and the limiting absorption principle are also presented. Chapter 3 is devoted to the transport or linearized Boltzmann equation, and in Chapter 4 the Lax and Phillips formalism is introduced in scattering theory for the transport equation. In their seminal book, Lax and Phillips introduced the incoming and outgoing subspaces, which verify their representation theorem for a dissipative hyperbolic system initially and also matches for the transport problem. By means of these subspaces, the Lax and Phillips semigroup is defined and it is proved that this semigroup is eventually compact, hence hyperbolic. Balanced equations give rise to two transport equations, one of which can satisfy an advection equation and one of which will be nonautonomous. For generating, the Howland semigroup and Howland's formalism must be used, as shown in Chapter 5. Chapter 6 is the highlight of the book, in which it is explained how the scattering operator for the transport problem by using the albedo operator can lead to recovery of the functionality of computerized tomography in medical science. The final chapter introduces the Wigner function, which connects the Schroedinger equation to statistical physics and the Husimi distribution function. Here, the relationship between the Wigner function and the quantum dynamical semigroup (QDS) can be seen.

The book provides a unifying insight into fluctuation phenomena in a broad variety of vibrational systems of current interest. It consists of individual chapters written by leading experts in the field. The chapters are self-contained and complement each other. The ongoing rapid development of well-characterized mesoscopic vibrational systems has made it possible to address fundamental physics problems and to explore new approaches to quantum and classical measurements, with applications to quantum information, condensed matter physics, and engineering. The book gives an account of major results in this direction. The topics include dynamics and quantum control of microcavity modes coupled to qubits, measurements with bifurcation-based amplifiers and new types of such amplifiers; switching rate scaling and new quantum mechanisms of metastable decay; wave mixing and parametric excitation in the quantum regime; collective phenomena and the interaction-induced discrete time symmetry breaking; and back-action and shot noise in electron-vibrational systems.

This book offers a modern way of dealing with the problems of equilibrium states of Bose systems. Starting with the variation principle of statistical mechanics and the energy-entropy balance principle as equilibrium criteria, results for general boson systems and models are explicitly derived using simple functional analytic calculus.

Bridging the gap between general theoretical physics and the phenomenological research in the field of Bose systems, this book provides an insight into the fascinating quantum world of bosons. Key topics include the occurrence of BEC and its intimate structural relation with the phenomena of spontaneous symmetry breaking and off-diagonal long range order; the condensate equation; the issue concerning the choice of boundary conditions; solvable versus non-solvable boson models; the set of quasi-free boson states; the role of dissipative perturbations; and the surprising but general relation between general quantum fluctuations and boson systems.

Only some knowledge of quantum mechanics and undergraduate algebra and analysis is assumed. This textbook brings students and researchers smoothly from general concepts to vivid applications.

Available here for the first time in English, "Reality and Its Order" is a remarkable philosophical text by Werner Heisenberg, the father of quantum mechanics and one of the leading scientists of the 20th century. Written during the wartime years and initially distributed only to his family and trusted friends, the essay describes Heisenberg's philosophical view of how we understand the natural world and our role within it. In this volume, the essay is introduced by the physicist Helmut Rechenberg and annotated by the science historian Ernst Peter Fischer. The content, particularly within its historical context, will be of great interest to many physicists, philosophers and historians of science.

This thesis presents a comprehensive theoretical description of classical and quantum aspects of plasmonics in three and two dimensions, and also in transdimensional systems containing elements with different dimensionalities. It focuses on the theoretical understanding of the salient features of plasmons in nanosystems as well as on the multifaceted aspects of plasmon-enhanced light-matter interactions at the nanometer scale. Special emphasis is given to the modeling of nonclassical behavior across the transition regime bridging the classical and the quantum domains. The research presented in this dissertation provides useful tools for understanding surface plasmons in various two- and three-dimensional nanostructures, as well as quantum mechanical effects in their response and their joint impact on light-matter interactions at the extreme nanoscale. These contributions constitute novel and solid advancements in the research field of plasmonics and nanophotonics that will help guide future experimental investigations in the blossoming field of nanophotonics, and also facilitate the design of the next generation of truly nanoscale nanophotonic devices.