With both industrial and teaching experience, the author explains the effects of time dependence in systems with two energy levels. The book starts with time-independent interactions and goes on to treat interactions with time-dependent electric and magnetic fields. Complete derivations are presented for each case, so the reader understands how the solutions are found. Both closed-form and numerical solutions are treated, and the calculations are compared with experimental data from the literature. Numerous plots are provided to show how the solutions depend on the parameters of the interactions.The book builds upon an undergraduate course in quantum mechanics and is useful for readers interested in magnetic resonance and quantum optics. In addition, this book is ideal for self-study by students or researchers starting on two-level systems. The detailed derivations and plots should ease readers into the study of two-level systems in a wide variety of settings.

'The book is a useful compendium of most significant topics in quantum information and computation ... It is readable by any undergraduate or graduate student in physics, mathematics, computer science, chemistry or engineering ... The book has a simple, attractive, easy to grasp and systematic treatment, with the final goal to be used as a substantial wide-ranging primer and single comprehensive material for quantum computation and information without the need for consulting supplementary texts.'Contemporary PhysicsQuantum computation and information is a rapidly developing interdisciplinary field. It is not easy to understand its fundamental concepts and central results without facing numerous technical details. This book provides the reader with a useful guide. In particular, the initial chapters offer a simple and self-contained introduction; no previous knowledge of quantum mechanics or classical computation is required.Various important aspects of quantum computation and information are covered in depth, starting from the foundations (the basic concepts of computational complexity, energy, entropy, and information, quantum superposition and entanglement, elementary quantum gates, the main quantum algorithms, quantum teleportation, and quantum cryptography) up to advanced topics (like entanglement measures, quantum discord, quantum noise, quantum channels, quantum error correction, quantum simulators and tensor networks).It can be used as a broad range textbook for a course in quantum information and computation, both for upper-level undergraduate students and for graduate students. It contains a large number of solved exercises, which are an essential complement to the text, as they will help the student to become familiar with the subject. The book may also be useful as general education for readers who want to know the fundamental principles of quantum information and computation and who have the basic background acquired from their undergraduate course in physics, mathematics, or computer science, as well as for researchers interested in some of the latest spin-off of the field, including the use of quantum information in the theories of many-body systems.

Thisvolumecontainsthewrittenversionsofinvitedlecturespresentedat the"39. InternationaleUniversitatswochenfur .. Kern-undTeilchenphysik"in Schladming, Austria, which took place from February 26th to March 4th, 2000. The title of the school was "Methods of Quantization". This is, of course,averybroad?eld,soonlysomeofthenewandinterestingdevel- mentscouldbecoveredwithinthescopeoftheschool. About75yearsagoSchrodingerpresentedhisfamouswaveequationand Heisenbergcameupwithhisalgebraicapproachtothequantum-theoretical treatmentofatoms. Aimingmainlyatanappropriatedescriptionofatomic systems, these original developments did not take into consideration E- stein'stheoryofspecialrelativity. WiththeworkofDirac,Heisenberg,and Pauliitsoonbecameobviousthatauni?edtreatmentofrelativisticandqu- tume?ectsisachievedbymeansoflocalquantum?eldtheory,i. e. anintrinsic many-particletheory. Mostofourpresentunderstandingoftheelementary buildingblocksofmatterandtheforcesbetweenthemisbasedonthequ- tizedversionof?eldtheorieswhicharelocallysymmetricundergaugetra- formations. Nowadays,theprevailingtoolsforquantum-?eldtheoreticalc- culationsarecovariantperturbationtheoryandfunctional-integralmethods. Beingnotmanifestlycovariant,theHamiltonianapproachtoquantum-?eld theorieslagssomewhatbehind,althoughitresemblesverymuchthefamiliar nonrelativisticquantummechanicsofpointparticles. Aparticularlyintere- ingHamiltonianformulationofquantum-?eldtheoriesisobtainedbyqu- tizingthe?eldsonhypersurfacesoftheMinkowsispacewhicharetangential tothelightcone. The"timeevolution"ofthesystemisthenconsideredin + "light-conetime"x =t+z/c. Theappealingfeaturesof"light-conequ- tization",whicharethereasonsfortherenewedinterestinthisformulation ofquantum?eldtheories,werehighlightedinthelecturesofBernardBakker andThomasHeinzl. Oneoftheopenproblemsoflight-conequantizationis theissueofspontaneoussymmetrybreaking. Thiscanbetracedbacktozero modeswhich,ingeneral,aresubjecttocomplicatedconstraintequations. A generalformalismforthequantizationofphysicalsystemswithconstraints waspresentedbyJohnKlauder. Theperturbativede?nitionofquantum?eld theoriesisingenerala?ictedbysingularitieswhichareovercomebyare- larizationandrenormalizationprocedure. Structuralaspectsoftherenormal- VI Preface izationprobleminthecaseofgaugeinvariant?eldtheorieswerediscussed inthelectureofKlausSibold. Areviewofthemathematicsunderlyingthe functional-integralquantizationwasgivenbyLudwigStreit. Apartfromthetopicsincludedinthisvolumetherewerealsolectures ontheKaluza-odingerpresentedhisfamouswaveequationand Heisenbergcameupwithhisalgebraicapproachtothequantum-theoretical treatmentofatoms. Aimingmainlyatanappropriatedescriptionofatomic systems, these original developments did not take into consideration E- stein'stheoryofspecialrelativity. WiththeworkofDirac,Heisenberg,and Pauliitsoonbecameobviousthatauni?edtreatmentofrelativisticandqu- tume?ectsisachievedbymeansoflocalquantum?eldtheory,i. e. anintrinsic many-particletheory. Mostofourpresentunderstandingoftheelementary buildingblocksofmatterandtheforcesbetweenthemisbasedonthequ- tizedversionof?eldtheorieswhicharelocallysymmetricundergaugetra- formations. Nowadays,theprevailingtoolsforquantum-?eldtheoreticalc- culationsarecovariantperturbationtheoryandfunctional-integralmethods. Beingnotmanifestlycovariant,theHamiltonianapproachtoquantum-?eld theorieslagssomewhatbehind,althoughitresemblesverymuchthefamiliar nonrelativisticquantummechanicsofpointparticles. Aparticularlyintere- ingHamiltonianformulationofquantum-?eldtheoriesisobtainedbyqu- tizingthe? eldsonhypersurfacesoftheMinkowsispacewhicharetangential tothelightcone. The"timeevolution"ofthesystemisthenconsideredin + "light-conetime"x =t+z/c. Theappealingfeaturesof"light-conequ- tization",whicharethereasonsfortherenewedinterestinthisformulation ofquantum?eldtheories,werehighlightedinthelecturesofBernardBakker andThomasHeinzl. Oneoftheopenproblemsoflight-conequantizationis theissueofspontaneoussymmetrybreaking. Thiscanbetracedbacktozero modeswhich,ingeneral,aresubjecttocomplicatedconstraintequations. A generalformalismforthequantizationofphysicalsystemswithconstraints waspresentedbyJohnKlauder. Theperturbativede?nitionofquantum?eld theoriesisingenerala?ictedbysingularitieswhichareovercomebyare- larizationandrenormalizationprocedure. Structuralaspectsoftherenormal- VI Preface izationprobleminthecaseofgaugeinvariant?eldtheorieswerediscussed inthelectureofKlausSibold. Areviewofthemathematicsunderlyingthe functional-integralquantizationwasgivenbyLudwigStreit. Apartfromthetopicsincludedinthisvolumetherewerealsolectures ontheKaluza-Kleinprogramforsupergravity(P. vanNieuwenhuizen),on dynamicalr-matricesandquantization(A. Alekseev),andonthequantum Liouvillemodelasaninstructiveexampleofquantumintegrablemodels(L. Faddeev). Inaddition,theschoolwascomplementedbymanyexcellents- inars. Thelistofseminarspeakersandthetopicsaddressedbythemcanbe foundattheendofthisvolume. Theinterestedreaderisrequestedtocontact thespeakersdirectlyfordetailedinformationorpertinentmaterial. Finally,wewouldliketoexpressourgratitudetothelecturersforalltheir e?ortsandtothemainsponsorsoftheschool,theAustrianMinistryofE- cation,Science,andCultureandtheGovernmentofStyria,forprovidingg- eroussupport. Wealsoappreciatethevaluableorganizationalandtechnical assistanceofthetownofSchladming,theSteyr-Daimler-PuchFahrzeugte- nik, Ricoh Austria, Styria Online, and the Hornig company. Furthermore, wethankoursecretaries,S. FuchsandE. Monschein,anumberofgra- atestudentsfromourinstitute,and,lastbutnotleast,ourcolleaguesfrom theorganizingcommitteefortheirassistanceinpreparingandrunningthe school. Graz, HeimoLatal March2001 WolfgangSchweiger Contents FormsofRelativisticDynamics BernardL. G. Bakker...1 1 Introduction...1 2 ThePoincar'eGroup...3 3 FormsofRelativisticDynamics...4 3. 1 ComparisonofInstantForm,FrontForm,andPointForm...6 4 Light-FrontDynamics...9 4. 1 RelativeMomentum,InvariantMass...9 4. 2 TheBoxDiagram...14 5 Poincar'eGeneratorsinFieldTheory...19 5. 1 FermionsInteractingwithaScalarField...20 5. 2 InstantForm...20 5. 3 FrontForm(LF)...21 5. 4 InteractingandNon-interactingGeneratorsonanInstant andontheLightFront...22 6 Light-FrontPerturbationTheory...23 6. 1 ConnectionofCovariantAmplitudes toLight-FrontAmplitudes...24 6. 2 Regularization...26 6. 3 MinusRegularization...26 7 TriangleDiagraminYukawaTheory...27 7. 1 CovariantCalculation ...28 7. 2 ConstructionoftheCurrentinLFD...30 7. 3 NumericalResults...37 3 8 FourVariationsonaThemein? Theory...37 8. 1 CovariantCalculation...39 8. 2 Instant-FormCalculation...42 8. 3 CalculationinLight-FrontCoordinates...47 8. 4 Front-FormCalculation...49 9 DimensionalRegularization:BasicFormulae...51 10 Four-DimensionalIntegration...52 11 SomeUsefulIntegrals...53 References...53 VIII Contents Light-ConeQuantization:FoundationsandApplications ThomasHeinzl...

'The authors should be recognised for their efforts to present a mathematically rigorous introduction to Quantum Mechanics (QM) in a form that has broad appeal; there are not many introductory QM texts that would cover, for example, decoherence. I think many educators would appreciate this book, especially those interested in courses that combine science and philosophy.'Contemporary PhysicsApart from providing a lucid introduction to the mathematical formalism and conceptual foundations of quantum mechanics, we explain why the laws of physics have the form that they do. In addition, we present a new and unique look at the quantum world, steering clear of two common errors: the error of the -ontologists, who reify a calculational tool; and the error of the anti-realists, for whom physical theories are simply devices for expressing regularities among observations.The new edition of this acclaimed text adds around 200 pages on a variety of topics, such as how the founders sought to make sense of quantum mechanics, Kant's theory of science, QBism, Everettian quantum mechanics, de Broglie-Bohm theory, environmental decoherence, contextuality, nonlocality, and the paradox of subjectivity - the curious fact that the world seems to exist twice, once for us, in our minds, and once by itself, independently of us.

Teaching quantum computation and information is notoriously difficult, because it requires covering subjects from various fields of science, organizing these subjects consistently in a unified way despite their tendency to favor their specific languages, and overcoming the subjects' abstract and theoretical natures, which offer few examples of actual realizations. In this book, we have organized all the subjects required to understand the principles of quantum computation and information processing in a manner suited to physics, mathematics, and engineering courses as early as undergraduate studies.In addition, we provide a supporting package of quantum simulation software from Wolfram Mathematica, specialists in symbolic calculation software. Throughout the book's main text, demonstrations are provided that use the software package, allowing the students to deepen their understanding of each subject through self-practice. Readers can change the code so as to experiment with their own ideas and contemplate possible applications. The information in this book reflects many years of experience teaching quantum computation and information. The quantum simulation-based demonstrations and the unified organization of the subjects are both time-tested and have received very positive responses from the students who have experienced them.

Motivates students by challenging them with real-life applications of the somtimes esoteric aspects of quantum mechanics that they are learning. Offers completely original excerices developed at teh Ecole Polytechnique in France, which is know for its innovative and original teaching methods. Problems from modern physics to help the student apply just-learnt theory to fields such as molecular physics, condensed matter physics or laser physics.

For many years, the physics of strongly correlated systems was considered a theorists' playground, right at the border with pure mathematics, where physicists from the real world' did not venture. The time has come, however, when healthy physics cannot exist without these techniques and results. Lectures on selected topics in the theory of strongly correlated systems are here presented by the leading experts in the field. Topics covered include a use of the form factor approach in low-dimensional systems, applications of quantum field theory to disorder, and dynamical mean field theory. The main divisions of the book deal with: I) Quantum Critical Points; (II) Strongly Correlated One-Dimensional Systems; (III) Strong Correlations and Disorder; and (IV) Dynamical Mean Field Theory.

This book presents quantum phononics as an exciting new field of research, and introduces readers to the quantum nature of phonons and their application to quantum technologies. Both the theory of and recent experiments in "quantum phononics," involving e.g. coherent phonons, phonon squeezing, coherent control, and phonon quantum technologies, are presented. The theoretical background of the generation and detection of phonons is described in a way that will be easy to understand for graduate students and experimental scientists who are newcomers to the field. Moreover, the book focuses on coherent phonons produced by ultrafast laser pulses, which can be used for the coherent control of atomic motions in solids and phase transformation. The laser-matter interaction is treated using a density matrix formalism of the time-dependent Schroeedinger equation. In addition, the third-order nonlinear optical response of condensed matter is also described.

This book describes a paradigm change in modern physics from the philosophy and mathematical expression of the quantum theory to those of general relativity. The approach applies to all domains - from elementary particles to cosmology. The change is from the positivistic views in which atomism, nondeterminism and measurement are fundamental, to a holistic view in realism, wherein matter - electrons, galaxies, - are correlated modes of a single continuum, the universe. A field that unifies electromagnetism, gravity and inertia is demonstrated explicitly, with new predictions, in terms of quaternion and spinor field equations in a curved spacetime. Quantum mechanics emerges as a linear, flatspace approximation for the equations of inertia in general relativity.

'Several features make this book unusual. The first is the historical content ... Second, the practical importance of quantum physics is demonstrated by the inclusion of numerous summary discussions of technological applications ... A third unusual feature of this book is a detailed solution immediately following each in-text exercise. Each such problem is used to advance the discussion, and the question-and-answer format encourages the student to wrestle with the ideas personally rather than simply reading passively ... This short book would easily make a helpful secondary text allowing an instructor to touch on some non-traditional topics such as least action principles and path integrals.'Contemporary PhysicsBridging the gap between traditional books on quantum and statistical physics, this series is an ideal introductory course for students who are looking for an alternative approach to the traditional academic treatment.This pedagogical approach relies heavily on scientific or technological applications from a wide range of fields. For every new concept introduced, an application is given to connect the theoretical results to a real-life situation. Each volume features in-text exercises and detailed solutions, with easy-to-understand applications.This first volume sets the scene of a new physics. It explains where quantum mechanics come from, its connection to classical physics and why it was needed at the beginning of the twentieth century. It examines how very simple models can explain a variety of applications such as quantum wells, thermoluminescence dating, scanning tunnel microscopes, quantum cryptography, masers, and how fluorescence can unveil the past of art pieces.

This volume deals with fundamental problems of the natural sciences and the philosophy of nature. The issues addressed touch upon the many research areas of Hans Primas, and they reflect both the depth and the breadth of his interests, ranging from nuclear magnetic resonance spectroscopy, theoretical chemistry, theory reduction, the measurement problem, holism and realism in quantum theory, to the dialogue between W. Pauli and C. G. Jung. Each individual contribution is prefaced by a short editorial introduction, relating diverse topics to each other and embedding them in a wider frame.

"I loved the book! This book is not just interesting, it is exciting. I have probably read every significant book in the field, and this is the strongest and most convincing one yet. It is also one of the most comprehensive in its explanations. I shall most certainly recommend the book to colleagues." -Richard G. Petty, MD "a very good introduction to the basic theory of quantum systems.... Dr. Georgiev's book aptly prepares the reader to confront whatever might be in store later." -from the Foreword by Prof. James F. Glazebrook, Eastern Illinois University This book addresses the fascinating cross-disciplinary field of quantum information theory applied to the study of brain function. It offers a self-study guide to probe the problems of consciousness, including a concise but rigorous introduction to classical and quantum information theory, theoretical neuroscience, and philosophy of the mind. It aims to address long-standing problems related to consciousness within the framework of modern theoretical physics in a comprehensible manner that elucidates the nature of the mind-body relationship. The reader also gains an overview of methods for constructing and testing quantum informational theories of consciousness.

"Scientists other than quantum physicists often fail to comprehend the enormity of the conceptual change wrought by quantum theory in our basic conception of the nature of matter," writes Henry Stapp. Stapp is a leading quantum physicist who has given particularly careful thought to the implications of the theory that lies at the heart of modern physics. In this book, which contains several of his key papers as well as new material, he focuses on the problem of consciousness and explains how quantum mechanics allows causally effective conscious thought to be combined in a natural way with the physical brain made of neurons and atoms. The book is divided into four sections. The first consists of an extended introduction. Key foundational and somewhat more technical papers are included in the second part, together with a clear exposition of the "orthodox" interpretation of quantum mechanics. The third part addresses, in a non-technical fashion, the implications of the theory for some of the most profound questions that mankind has contemplated: How does the world come to be just what it is and not something else? How should humans view themselves in a quantum universe? What will be the impact on society of the revised scientific image of the nature of man? The final part contains a mathematical appendix for the specialist and a glossary of important terms and ideas for the interested layman. This third edition has been significantly expanded with two new chapters covering the author's most recent work.

An important contributor to our current understanding of critical phenomena, Ma introduces the beginner--especially the graduate student with no previous knowledge of the subject-to fundamental theoretical concepts such as mean field theory, the scaling hypothesis, and the renormalization group. He then goes on to apply the renormalization group to selected problems, with emphasis on the underlying physics and the basic assumptions involved.

Fractional quantum mechanics is a recently emerged and rapidly developing field of quantum physics.This is the first monograph on fundamentals and physical applications of fractional quantum mechanics, written by its founder.The fractional Schroedinger equation and the fractional path integral are new fundamental physical concepts introduced and elaborated in the book. The fractional Schroedinger equation is a manifestation of fractional quantum mechanics. The fractional path integral is a new mathematical tool based on integration over Levy flights. The fractional path integral method enhances the well-known Feynman path integral framework.Related topics covered in the text include time fractional quantum mechanics, fractional statistical mechanics, fractional classical mechanics and the -stable Levy random process.The book is well-suited for theorists, pure and applied mathematicians, solid-state physicists, chemists, and others working with the Schroedinger equation, the path integral technique and applications of fractional calculus in various research areas. It is useful to skilled researchers as well as to graduate students looking for new ideas and advanced approaches.

The authors examine topics in modern physics and offer a unitary and original treatment of the fundamental problems of the dynamics of physical systems, as well as a description of the nuclear matter within a framework of general relativity. They show that some physical phenomena studied at two different resolution scales (e.g. microscale, cosmological scale), apparently with no connection between them, become compatible by means of the operational procedures, acting either as some "hidden" symmetries, or harmonic-type mappings. The book is addressed to the students, researchers and university/high school teachers working in the fields of mathematics, physics, and chemistry.

Presenting the proceedings of FPCP 2018, this book reviews the status quo of flavor physics and discusses the latest findings in this exciting area. Flavor physics has been instrumental in the formulation and understanding of the standard model, and it is possible that the direction of new physics will be significantly influenced by flavor sector, also known as the intensity frontier, making it possible to indirectly test the existence of new physics up to a very high scale, beyond that of the energy frontier scale accessible at the LHC. The book is intended for academics around the globe involved in particle physics research, professionals associated with the related technologies and those who are interested in learning about the future of physics and its prospects and directions.

This present edition of the book follows the generally pedagogic style of Quantum Mechanics. The scope ranges from relativistic quantum mechanics to an introduction to quantum field theory with quantum electrodynamics as the basic example and ends with an exposition of important issues related to the standard model. The book presents the subject in basic and easy-to-grasp notions which will enhance the purpose of this book as a useful textbook in the area of relativistic quantum mechanics and quantum electrodynamics.

The topics in this volume include the ideas of mathematicians, physicists and chemists in the area of multiparticle scattering theory. Scattering theory (or collision theory as it is often called) is a fundamental area of theory and computation in both physics and chemistry. The correct formulation of scattering theory for two-body collisions is now well worked out, but systems with three or more particles still present fundamental unmet challenges, both in the formulations of the problem and in the interpretation of computational results. A key issue in the mathematical foundations is asymptotic completeness, which says that any state of a quantum system is a superposition of bound and scattering states. Key issues on the physical side are concerned with boundary conditions, electromagnetic fields, effective potentials and resonances.

Does the universe embody beautiful ideas? Artists as well as scientists throughout human history have pondered this "beautiful question." With Nobel laureate Frank Wilczek as your guide, embark on a voyage of related discoveries, from Plato and Pythagoras up to the present. Wilczek's groundbreaking work in quantum physics was inspired by his intuition to look for a deeper order of beauty in nature. This is the deep logic of the universe-and it is no accident that it is also at the heart of what we find aesthetically pleasing and inspiring. Wilczek is hardly alone among great scientists in charting his course using beauty as his compass. As he reveals in A Beautiful Question, this has been the heart of scientific pursuit from Pythagoras and the ancient belief in the music of the spheres to Galileo, Newton, Maxwell, Einstein, and into the deep waters of twentieth-century physics. Wilczek brings us right to the edge of knowledge today, where the core insights of even the craziest quantum ideas apply principles we all understand. The equations for atoms and light are almost the same ones that govern musical instruments and sound; the subatomic particles that are responsible for most of our mass are determined by simple geometric symmetries. Gorgeously illustrated, A Beautiful Question is a mind-shifting book that braids the age-old quest for beauty and the age-old quest for truth into a thrilling synthesis. It is a dazzling and important work from one of our best thinkers, whose humor and infectious sense of wonder animate every page. Yes: The world is a work of art, and its deepest truths are ones we already feel, as if they were somehow written in our souls.

The work studies under different physical conditions the carrier contribution to elastic constants in heavily doped optoelectronic materials. In the presence of intense photon field the authors apply the Heisenberg Uncertainty Principle to formulate electron statistics. Many open research problems are discussed and numerous potential applications as quantum sensors and quantum cascade lasers are presented.

While theoretical particle physics is an extraordinarily fascinating field, the incredibly fast pace at which it moves along, combined with the huge amount of background information necessary to perform cutting edge research, poses a formidable challenge for graduate students.

This book represents the first in a series designed to assist students in the process of transitioning from coursework to research in particle physics. Rather than reading literally dozens of physics and mathematics texts, trying to assimilate the countless ideas, translate notations and perspectives, and see how it all fits together to get a holistic understanding, this series provides a detailed overview of the major mathematical and physical ideas in theoretical particle physics. Ultimately the ideas will be presented in a unified, consistent, holistic picture, where each topic is built firmly on what has come before, and all topics are related in a clear and intuitive way.

This introductory text on quantum field theory and particle physics provides both a self-contained and complete introduction to not only the necessary physical ideas, but also a complete introduction to the necessary mathematical tools. Assuming minimal knowledge of undergraduate physics and mathematics, this book lays both the mathematical and physical groundwork with clear, intuitive explanations and plenty of examples. The book then continues with an exposition of the Standard Model of Particle Physics, the theory that currently seems to explain the universe apart from gravity. Furthermore, this book was written as a primer for the more advanced mathematical and physical ideas to come later in this series.

Quantum Chromodynamics (QCD) describes the interactions between elementary quarks and gluons as they compose the nucleons at the heart of atomic structure. The interactions give rise to complexity that can only be examined via numerical simulations on supercomputers. This work provides an introduction to the numerical simulations of lattice QCD and establishes new formalisms relevant to understanding the structure of nucleons and their excited states. The research opens with an examination of the non-trivial QCD vacuum and the emergence of "centre domains." The focus then turns to establishing a novel Parity-Expanded Variational Analysis (PEVA) technique solving the important problem of isolating baryon states moving with finite momentum. This seminal work provides a foundation for future calculations of baryon properties. Implementation of the PEVA formalism discloses important systematic errors in conventional calculations and reveals the structure of nucleon excited states from the first principles of QCD for the first time.

'The authors have done an exceptional job. ItaEURO (TM)s probably more accurate to describe this text as an introduction to both non-relativistic and relativistic quantum mechanics ... This book was a lot of fun to read and digest. I definitely recommend it for instructors, but also for students who have already been exposed to quantum mechanics.'Contemporary PhysicsThis book is a revised and updated version of Introductory Quantum Physics and Relativity. Based on lectures given as part of the undergraduate degree programme at the University of Leeds, it has been extended in line with recent developments in the field. The book contains all the material required for quantum physics and relativity in the first three years of a traditional physics degree, in addition to more interesting and up-to-date extensions and applications which include quantum field theory, entanglement, and quantum information science.The second edition is unique as an undergraduate textbook as it combines quantum physics and relativity at an introductory level. It expounds the foundations of these two subjects in detail, but also illustrates how they can be combined. It discusses recent applications, but also exposes undergraduates to cutting-edge research topics, such as laser cooling, Bose-Einstein condensation, tunneling microscopes, lasers, nonlocality, and quantum teleportation.