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.

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.

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."

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.

With the exponential growth of program trading in the global financial industry, quantum finance and its underlying technologies have become one of the hottest topics in the fintech community. Numerous financial institutions and fund houses around the world require computer professionals with a basic understanding of quantum finance to develop intelligent financial systems. This book presents a selection of the author's past 15 years' R&D work and practical implementation of the Quantum Finance Forecast System - which integrates quantum field theory and related AI technologies to design and develop intelligent global financial forecast and quantum trading systems. The book consists of two parts: Part I discusses the basic concepts and theories of quantum finance and related AI technologies, including quantum field theory, quantum price fields, quantum price level modelling and quantum entanglement to predict major financial events. Part II then examines the current, ongoing R&D projects on the application of quantum finance technologies in intelligent real-time financial prediction and quantum trading systems. This book is both a textbook for undergraduate & masters level quantum finance, AI and fintech courses and a valuable resource for researchers and data scientists working in the field of quantum finance and intelligent financial systems. It is also of interest to professional traders/ quants & independent investors who would like to grasp the basic concepts and theory of quantum finance, and more importantly how to adopt this fascinating technology to implement intelligent financial forecast and quantum trading systems. For system implementation, the interactive quantum finance programming labs listed on the Quantum Finance Forecast Centre official site (QFFC.org) enable readers to learn how to use quantum finance technologies presented in the book.

The field of quantum computing has experienced rapid development and many different experimental and theoretical groups have emerged worldwide.This book presents the key elements of quantum computation and communication theories and their implementation in an easy-to-read manner for readers coming from physics, mathematics and computer science backgrounds. Integrating both theoretical aspects and experimental verifications of developing quantum computers, the author explains why particular mathematical methods, physical models and realistic implementations might provide critical steps towards achieving the final goal - constructing quantum computers and quantum networks. The book serves as an excellent introduction for new researchers and also provides a useful review for specialists in the field

This thesis uses the tools of quantum information science to uncover fascinating new insights about the intersection of quantum theory and relativity. It is divided into three self-contained parts, the first of which employs detector models to investigate how the information content of quantum fields depends on spacetime curvature and global spacetime topology. The behavior of Unruh-DeWitt detectors on curved spacetimes are investigated, following which these detectors are used to probe the vacuum state of a scalar field in various topologies. This leads to a generalization of the entanglement harvesting protocol involving detectors in arbitrary curved spacetimes admitting a Wightman function. The second part extends the theory of quantum reference frames to those associated with noncompact groups. Motivated by the pursuit of a relational relativistic quantum theory where the group of reference frames is the Poincare group, the author then generalizes a communication protocol between two parties lacking a common reference frame to the scenario where the group of transformations of their reference frame is a one-dimensional noncompact Lie group. Finally, the third part, inspired by theories of quantum gravity, generalizes the conditional probability interpretation of time, a proposed mechanism for time to emerge from a fundamentally timeless Universe. While the conditional probability interpretation of time is based upon conditioning a solution to the Wheeler-DeWitt equation on a subsystem of the universe that acts a clock, the author extends this approach to include an interaction between the system being used as a clock and a system whose evolution the clock is tracking.

"Quantum Phenomena do not occur in a Hilbert space. They occur in a laboratory". - Asher Peres Semiconductor physics is a laboratory to learn and discover the concepts of quantum mechanics and thermodynamics, condensed matter physics, and materials science, and the payoffs are almost immediate in the form of useful semiconductor devices. Debdeep Jena has had the opportunity to work on both sides of the fence - on the fundamental materials science and quantum physics of semiconductors, and in their applications in semiconductor electronic and photonic devices. In Quantum Physics of Semiconductors and Nanostructures, Jena uses this experience to make each topic as tangible and accessible as possible to students at all levels. Consider the simplest physical processes that occur in semiconductors: electron or hole transport in bands and over barriers, collision of electrons with the atoms in the crystal, or when electrons and holes annihilate each other to produce a photon. The correct explanation of these processes require a quantum mechanical treatment. Any shortcuts lead to misconceptions that can take years to dispel, and sometimes become roadblocks towards a deeper understanding and appreciation of the richness of the subject. A typical introductory course on semiconductor physics would then require prerequisites of quantum mechanics, statistical physics and thermodynamics, materials science, and electromagnetism. Rarely would a student have all this background when (s)he takes a course of this nature in most universities. Jena's work fills in these gaps and gives students the background and deeper understanding of the quantum physics of semiconductors and nanostructures.

This book presents a history of the correspondence principle from a new perspective. The author provides a unique exploration of the relation between the practice of theory and conceptual development in physics. In the process, he argues for a new understanding of the history of the old quantum theory and the emergence of quantum mechanics. The analysis looks at how the correspondence principle was disseminated and how the principle was applied as a research tool during the 1920s. It provides new insights into the interaction between theoretical tools and scientific problems and shows that the use of this theoretical tool changed the tool itself in a process of transformation through implementation. This process, the author claims, was responsible for the conceptual development of the correspondence principle. This monograph connects to the vast literature in the history of science, which analyzed theoretical practices as based on tacit knowledge, skills, and calculation techniques. It contributes to the historical understanding of quantum physics and the emergence of quantum mechanics. Studying how physicists used a set of tools to solve problems, the author spells out the skillful guessing" that went into the making of quantum theoretical arguments and argues that the integration and implementation of technical resources was a central driving force for the conceptual and theoretical transformation in the old quantum theory.

This book presents an exhaustive study of atomicity from a mathematics perspective in the framework of multi-valued non-additive measure theory. Applications to quantum physics and, more generally, to the fractal theory of the motion, are highlighted. The study details the atomicity problem through key concepts, such as the atom/pseudoatom, atomic/nonatomic measures, and different types of non-additive set-valued multifunctions. Additionally, applications of these concepts are brought to light in the study of the dynamics of complex systems. The first chapter prepares the basics for the next chapters. In the last chapter, applications of atomicity in quantum physics are developed and new concepts, such as the fractal atom are introduced. The mathematical perspective is presented first and the discussion moves on to connect measure theory and quantum physics through quantum measure theory. New avenues of research, such as fractal/multifractal measure theory with potential applications in life sciences, are opened.

The contributions gathered here demonstrate how categorical ontology can provide a basis for linking three important basic sciences: mathematics, physics, and philosophy. Category theory is a new formal ontology that shifts the main focus from objects to processes. The book approaches formal ontology in the original sense put forward by the philosopher Edmund Husserl, namely as a science that deals with entities that can be exemplified in all spheres and domains of reality. It is a dynamic, processual, and non-substantial ontology in which all entities can be treated as transformations, and in which objects are merely the sources and aims of these transformations. Thus, in a rather surprising way, when employed as a formal ontology, category theory can unite seemingly disparate disciplines in contemporary science and the humanities, such as physics, mathematics and philosophy, but also computer and complex systems science.

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."

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.

This book explains the group representation theory for quantum theory in the language of quantum theory. As is well known, group representation theory is very strong tool for quantum theory, in particular, angular momentum, hydrogen-type Hamiltonian, spin-orbit interaction, quark model, quantum optics, and quantum information processing including quantum error correction. To describe a big picture of application of representation theory to quantum theory, the book needs to contain the following six topics, permutation group, SU(2) and SU(d), Heisenberg representation, squeezing operation, Discrete Heisenberg representation, and the relation with Fourier transform from a unified viewpoint by including projective representation. Unfortunately, although there are so many good mathematical books for a part of six topics, no book contains all of these topics because they are too segmentalized. Further, some of them are written in an abstract way in mathematical style and, often, the materials are too segmented. At least, the notation is not familiar to people working with quantum theory. Others are good elementary books, but do not deal with topics related to quantum theory. In particular, such elementary books do not cover projective representation, which is more important in quantum theory. On the other hand, there are several books for physicists. However, these books are too simple and lack the detailed discussion. Hence, they are not useful for advanced study even in physics. To resolve this issue, this book starts with the basic mathematics for quantum theory. Then, it introduces the basics of group representation and discusses the case of the finite groups, the symmetric group, e.g. Next, this book discusses Lie group and Lie algebra. This part starts with the basics knowledge, and proceeds to the special groups, e.g., SU(2), SU(1,1), and SU(d). After the special groups, it explains concrete applications to physical systems, e.g., angular momentum, hydrogen-type Hamiltonian, spin-orbit interaction, and quark model. Then, it proceeds to the general theory for Lie group and Lie algebra. Using this knowledge, this book explains the Bosonic system, which has the symmetries of Heisenberg group and the squeezing symmetry by SL(2,R) and Sp(2n,R). Finally, as the discrete version, this book treats the discrete Heisenberg representation which is related to quantum error correction. To enhance readers' undersnding, this book contains 54 figures, 23 tables, and 111 exercises with solutions.

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.

This Open Access book gives a comprehensive account of both the history and current achievements of molecular beam research. In 1919, Otto Stern launched the revolutionary molecular beam technique. This technique made it possible to send atoms and molecules with well-defined momentum through vacuum and to measure with high accuracy the deflections they underwent when acted upon by transversal forces. These measurements revealed unforeseen quantum properties of nuclei, atoms, and molecules that became the basis for our current understanding of quantum matter. This volume shows that many key areas of modern physics and chemistry owe their beginnings to the seminal molecular beam work of Otto Stern and his school. Written by internationally recognized experts, the contributions in this volume will help experienced researchers and incoming graduate students alike to keep abreast of current developments in molecular beam research as well as to appreciate the history and evolution of this powerful method and the knowledge it reveals.

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 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.

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.

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 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.

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 book explains the evolution of techniques and strategies in quantum computing, discussing the digital transition towards the quantum computing application in various sectors. The book provides a comprehensive insight into the quantum mechanics and quantum computing techniques and tools and how they have evolved and the impacted in supporting and flourishing business during the quantum computing era. This book includes chapters that discuss the most primitive quantum schemes to the most recent use of Internet, finance and radar technology, thus leveraging greater use of new technologies like security and Internet and others. The content is relevant for an audience that is involved in the research and development of advanced quantum systems. It gives the industry, researchers, and students interested in learning the various quantum computing sectors with the necessary information and tools that can be used to research, design and develop advanced quantum computing systems and techniques.

This thesis presents the first experimental calibration of the top-quark Monte-Carlo mass. It also provides the top-quark mass-independent and most precise top-quark pair production cross-section measurement to date. The most precise measurements of the top-quark mass obtain the top-quark mass parameter (Monte-Carlo mass) used in simulations, which are partially based on heuristic models. Its interpretation in terms of mass parameters used in theoretical calculations, e.g. a running or a pole mass, has been a long-standing open problem with far-reaching implications beyond particle physics, even affecting conclusions on the stability of the vacuum state of our universe. In this thesis, this problem is solved experimentally in three steps using data obtained with the compact muon solenoid (CMS) detector. The most precise top-quark pair production cross-section measurements to date are performed. The Monte-Carlo mass is determined and a new method for extracting the top-quark mass from theoretical calculations is presented. Lastly, the top-quark production cross-sections are obtained - for the first time - without residual dependence on the top-quark mass, are interpreted using theoretical calculations to determine the top-quark running- and pole mass with unprecedented precision, and are fully consistently compared with the simultaneously obtained top-quark Monte-Carlo mass.

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.