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Elementarteilchen: Eine Einführung für Naturwissenschaftler

Die Autoren beginnen mit einem historischen Rückblick auf die Entstehung der modernen Physik und die ersten Erfolge bei der Beschreibung der vier fundamentalen Kräfte der Natur: der Elektrodynamik, der Schwachen und Starken Kernkräfte und der Schwerkraft. Die Darstellung der großen Fortschritte der 60er und 70er Jahre mit der Entstehung des Standardmodells der Elementarteilchenphysik ist im Aufbau eher systematisch. Der Schwerpunkt liegt aber stets auf der Einführung des Lesers in die Konzepte und Begriffe dieser Wissenschaft, ohne aber den mathematischen Apparat in Anspruch zu nehmen. Wie die zahlreichen Bilder dienen die Formeln eher zur Illustration des Textes und stellen keine strengen Herleitungen dar. Im abschließenden Kapitel wird versucht, den derzeitigen Forschungsstand wiederzugeben und die aktuellen Bemühungen der Physiker um ein besseres Verständnis der Kräfte der Natur vorzustellen.

Elementarteilchen und ihre Wechselwirkungen: Eine Übersicht

Die dritte Auflage dieses bewährten Lehrbuchs bietet in seiner gründlichen Überarbeitung und mit zahlreichen Ergänzungen eine konzise Übersicht über die Physik der Elementarteilchen und ihrer Wechselwirkungen. Die Autoren - beide Wissenschaftler mit langjähriger und umfassender Forschungs- und Lehrerfahrung an renommierten Einrichtungen - stellen in einzigartiger Weise den Kanon der Elementarteilchenphysik gleichzeitig verständlich und übersichtlich zusammen. Das Lehrbuch dient der effizienten Prüfungsvorbereitung, ist aber auch zum Nachschlagen für Diplom- und Doktorarbeiten geeignet, dies nicht zuletzt dank des umfangreichen Tabellenanhangs.

Elementarteilchen und ihre Wechselwirkungen: Eine Übersicht

Die dritte Auflage dieses bewährten Lehrbuchs bietet in seiner gründlichen Überarbeitung und mit zahlreichen Ergänzungen eine konzise Übersicht über die Physik der Elementarteilchen und ihrer Wechselwirkungen. Die Autoren - beide Wissenschaftler mit langjähriger und umfassender Forschungs- und Lehrerfahrung an renommierten Einrichtungen - stellen in einzigartiger Weise den Kanon der Elementarteilchenphysik gleichzeitig verständlich und übersichtlich zusammen. Das Lehrbuch dient der effizienten Prüfungsvorbereitung, ist aber auch zum Nachschlagen für Diplom- und Doktorarbeiten geeignet, dies nicht zuletzt dank des umfangreichen Tabellenanhangs.

Elementarteilchenphysik: Von den Grundlagen zu den modernen Experimenten (Springer-Lehrbuch)

Systematische Einführung, von den Grundlagen zu den modernen Experimenten bis zu den jüngsten Entwicklungen des Gebiets. Experimentelle Hilfsmittel wie Beschleuniger und Detektoren werden zu Beginn besprochen. Dann folgen die Symmetrieprinzipien und ihre Anwendungen. Neueste experimentelle Ergebnisse zur Neutrinophysik und zur Verletzung der CP-Symmetrie werden behandelt, bevor die Frage nach möglichen Erweiterungen des Standardmodells gestellt wird. Ansprechende Gestaltung mit 88 Übungen und Lösungshinweisen.

Elementarteilchenphysik: Von den Grundlagen zu den modernen Experimenten (Springer-Lehrbuch)

Dieses Lehrbuch bietet eine systematische Einführung, von den Grundlagen zu den modernen Experimenten bis hin zu den jüngsten Entwicklungen des Gebiets. Experimentelle Hilfsmittel wie Beschleuniger und Detektoren werden zu Beginn besprochen. Dann folgen die Symmetrieprinzipien und ihre Anwendungen. Im folgenden wird das Standardmodell entwickelt, das die heutige experimentelle und theoretische Diskussion weitgehend beherrscht. Hierzu werden wesentliche Bereiche der Quantenelektrodynamik, des Quarkmodells, der Quantenchromodynamik und der elektroschwachen Theorie erläutert. Neueste experimentelle Ergebnisse zur Neutrinophysik und zur Verletzung der CP-Symmetrie werden behandelt, bevor die Frage nach möglichen Erweiterungen des Standardmodells gestellt wird. Das Lehrbuch ist ansprechend gestaltet, 88 Übungen mit Lösungshinweisen dienen der Vertiefung.

Elementarteilchenphysik: Von den Grundlagen zu den modernen Experimenten (Springer-Lehrbuch)

Systematische Einführung, von den Grundlagen zu den modernen Experimenten bis zu den jüngsten Entwicklungen des Gebiets. Experimentelle Hilfsmittel wie Beschleuniger und Detektoren werden zu Beginn besprochen. Dann folgen die Symmetrieprinzipien und ihre Anwendungen. Neueste experimentelle Ergebnisse zur Neutrinophysik und zur Verletzung der CP-Symmetrie werden behandelt, bevor die Frage nach möglichen Erweiterungen des Standardmodells gestellt wird. Ansprechende Gestaltung mit 88 Übungen und Lösungshinweisen.

Elementary: The Periodic Table Explained

The periodic table, created in the early 1860s by Russian chemist Dmitri Mendeleev, marked one of the most extraordinary advances in modern chemistry. This basic visual aid helped scientists to gain a deeper understanding of what chemical elements really were: and, astonishingly, it also correctly predicted the properties of elements that hadn’t been discovered at the time.Here, in the authoritative Elementary, James Russell uses his lively, accessible and engaging narrative to tell the story behind all the elements we now know about. From learning about the creation of the first three elements, hydrogen, lithium and helium, in the big bang, through to oxygen and carbon, which sustain life on earth – along with the many weird and wonderful uses of elements as varied as fluorine, arsenic, krypton and einsteinium – even the most unscientifically minded will be enthralled by this fascinating subject. Russell compellingly details these most basic building blocks of the universe, and the people who identified, isolated and even created them.

Elementary Approach to Special Relativity

This book presents an alternative representation of Einstein's Special Theory of Relativity, which makes Special Relativity much more comprehensible. Moreover, one will come across a fundamental relationship between the Special Theory of Relativity and the mechanics of space lattice. In all previous formulations, the Einsteinian special principle of relativity, in one or the other form is used as the starting point for Special Relativity. In correspondence to this principle, one takes it as granted apriori, that all observers independent of their uniform motion to each other measure one and the same propagation velocity of a light signal. This book is thought of as a lecture for physicists, mathematicians and computer scientists and concentrates on the students of these fields. The book should reach a broad circle of interested readers from the fields of natural sciences and philosophy and provide and invigorating experience for engineers.

Elementary Chemical Thermodynamics

This straightforward presentation emphasizes chemical applications of thermodynamics as well as physical interpretations, offering students an introduction that's both interesting and coherent. It considers chemical behavior in terms of energy and entropy, and it explains the ways in which the magnitude of energy and entropy changes are dictated by atomic properties. All concepts are presented in a simplified mathematical context, making this an ideal text for a beginning course in thermodynamics.The author considers the first and second laws of thermodynamics in turn, after which he proceeds to applications of thermodynamic principles. He devotes considerable attention to the concept of entropy, emphasizing the interpretation of entropy changes and chemical behavior in terms of qualitative molecular properties. Students gain a familiarity with the entropy concept that will form a solid foundation for later courses and more formal thermodynamic treatments.

Elementary Cluster Analysis: Four Basic Methods that (Usually) Work

The availability of packaged clustering programs means that anyone with data can easily do cluster analysis on it. But many users of this technology don't fully appreciate its many hidden dangers. In today's world of "grab and go algorithms," part of my motivation for writing this book is to provide users with a set of cautionary tales about cluster analysis, for it is very much an art as well as a science, and it is easy to stumble if you don't understand its pitfalls. Indeed, it is easy to trip over them even if you do! The parenthetical word usually in the title is very important, because all clustering algorithms can and do fail from time to time. Modern cluster analysis has become so technically intricate that it is often hard for the beginner or the non-specialist to appreciate and understand its many hidden dangers. Here's how Yogi Berra put it, and he was right: In theory there's no difference between theory and practice. In practice, there is ~Yogi Berra This book is a step backwards, to four classical methods for clustering in small, static data sets that have all withstood the tests of time. The youngest of the four methods is now almost 50 years old: Gaussian Mixture Decomposition (GMD, 1898) SAHN Clustering (principally single linkage (SL, 1909)) Hard c-means (HCM, 1956, also widely known as (aka) "k-means") Fuzzy c-means (FCM, 1973, reduces to HCM in a certain limit) The dates are the first known writing (to me, anyway) about these four models. I am (with apologies to Marvel Comics) very comfortable in calling HCM, FCM, GMD and SL the Fantastic Four. Cluster analysis is a vast topic. The overall picture in clustering is quite overwhelming, so any attempt to swim at the deep end of the pool in even a very specialized subfield requires a lot of training. But we all start out at the shallow end (or at least that's where we should start!), and this book is aimed squarely at teaching toddlers not to be afraid of the water. There is no section of this book that, if explored in real depth, cannot be expanded into its own volume. So, if your needs are for an in-depth treatment of all the latest developments in any topic in this volume, the best I can do - what I will try to do anyway - is lead you to the pool, and show you where to jump in.

Elementary Cluster Analysis: Four Basic Methods that (Usually) Work

The availability of packaged clustering programs means that anyone with data can easily do cluster analysis on it. But many users of this technology don't fully appreciate its many hidden dangers. In today's world of "grab and go algorithms," part of my motivation for writing this book is to provide users with a set of cautionary tales about cluster analysis, for it is very much an art as well as a science, and it is easy to stumble if you don't understand its pitfalls. Indeed, it is easy to trip over them even if you do! The parenthetical word usually in the title is very important, because all clustering algorithms can and do fail from time to time. Modern cluster analysis has become so technically intricate that it is often hard for the beginner or the non-specialist to appreciate and understand its many hidden dangers. Here's how Yogi Berra put it, and he was right: In theory there's no difference between theory and practice. In practice, there is ~Yogi Berra This book is a step backwards, to four classical methods for clustering in small, static data sets that have all withstood the tests of time. The youngest of the four methods is now almost 50 years old: Gaussian Mixture Decomposition (GMD, 1898) SAHN Clustering (principally single linkage (SL, 1909)) Hard c-means (HCM, 1956, also widely known as (aka) "k-means") Fuzzy c-means (FCM, 1973, reduces to HCM in a certain limit) The dates are the first known writing (to me, anyway) about these four models. I am (with apologies to Marvel Comics) very comfortable in calling HCM, FCM, GMD and SL the Fantastic Four. Cluster analysis is a vast topic. The overall picture in clustering is quite overwhelming, so any attempt to swim at the deep end of the pool in even a very specialized subfield requires a lot of training. But we all start out at the shallow end (or at least that's where we should start!), and this book is aimed squarely at teaching toddlers not to be afraid of the water. There is no section of this book that, if explored in real depth, cannot be expanded into its own volume. So, if your needs are for an in-depth treatment of all the latest developments in any topic in this volume, the best I can do - what I will try to do anyway - is lead you to the pool, and show you where to jump in.

Elementary Continuum Mechanics for Everyone: With Applications to Structural Mechanics (Solid Mechanics and Its Applications #194)

The book opens with a derivation of kinematically nonlinear 3-D continuum mechanics for solids. Then the principle of virtual work is utilized to derive the simpler, kinematically linear 3-D theory and to provide the foundation for developing consistent theories of kinematic nonlinearity and linearity for specialized continua, such as beams and plates, and finite element methods for these structures. A formulation in terms of the versatile Budiansky-Hutchinson notation is used as basis for the theories for these structures and structural elements, as well as for an in-depth treatment of structural instability.

Elementary engineering fracture mechanics

When asked to start teaching a course on engineering fracture mechanics, I realized that a concise textbook, giving a general oversight of the field, did not exist. The explanation is undoubtedly that the subject is still in a stage of early development, and that the methodologies have still a very limited applicability. It is not possible to give rules for general application of fracture mechanics concepts. Yet our comprehension of cracking and fracture beha viour of materials and structures is steadily increasing. Further developments may be expected in the not too distant future, enabling useful prediction of fracture safety and fracture characteristics on the basis of advanced fracture mechanics procedures. The user of such advanced procedures m\lst have a general understanding of the elementary concepts, which are provided by this volume. Emphasis was placed on the practical application of fracture mechanics, but it was aimed to treat the subject in a way that may interest both metallurgists and engineers. For the latter, some general knowledge of fracture mechanisms and fracture criteria is indispensable for an apprecia­ tion of the limita tions of fracture mechanics. Therefore a general discussion is provided on fracture mechanisms, fracture criteria, and other metal­ lurgical aspects, without going into much detail. Numerous references are provided to enable a more detailed study of these subjects which are still in a stage of speculative treatment.

Elementary Excitations in Quantum Fluids: Proceedings of the Hiroshima Symposium, Hiroshima, Japan, August 17–18, 1987 (Springer Series in Solid-State Sciences #79)

This volume is the proceedings of the Hiroshima Symposium on Elementary Excitations in Quantum Fluids, which was held on August 17 and 18, 1987, in Hiroshima, Japan, and was attended by thirty-two scientists from seven countries. Quantum fluids have been the subject of intense study as a consequence of their superfluid properties at very low temperatures. Elementary excitations in them are an important concept about which many important discoveries have been made in recent years. This symposium was arranged by a group of physicists from Hiroshima University to provide an opportunity to discuss these recent developments. It was conceived as a satellite conference of the 18th International Conference on Low Temperature Physics (LT 18), which was held in Kyoto, August 20-26, 1987. Emphasis was placed on the dynamic structures and correlations of ele­ mentary excitations, which resulted in invited speakers being selected from this field. However, enthusiastic contributors reported notable new results on various other aspects of the elementary excitations, which made the sympo­ sium lively and successful. It is our great satisfaction to present this volume, which includes papers of good quality and originality. We thank all the parti­ cipants for their cooperation throughout this symposium, and for preparing their manuscripts within a reasonable time.

Elementary Excitations In Solids

This text continues to fill the need to communicate the present view of a solid as a system of interacting particles which, under suitable circumstances, behaves like a collection of nearly independent elementary excitations. In addition to introducing basic concepts, the author frequently refers to experimental data. Usually, both the basic theory and the applications discussed deal with the behavior of '`'simple' metals, rather than the '`'complicated' metals, such as the transition metals and the rare earths. Problems have been included for most of the chapters.

Elementary Excitations In Solids: Lectures On Protons, Electrons, And Plasmons

This text continues to fill the need to communicate the present view of a solid as a system of interacting particles which, under suitable circumstances, behaves like a collection of nearly independent elementary excitations. In addition to introducing basic concepts, the author frequently refers to experimental data. Usually, both the basic theory and the applications discussed deal with the behavior of '`'simple' metals, rather than the '`'complicated' metals, such as the transition metals and the rare earths. Problems have been included for most of the chapters.

Elementary Excitations in Solids, Molecules, and Atom: Part B (pdf) (Nato ASI Subseries B: #2)

Elementary Excitations in Solids, Molecules, and Atoms: Part A (Nato Science Series B: #2)

The Advanced Study Institute on 'Elementary Excitations in Solids, Molecules, and Atoms' was held at the University of Antwerp (U.I.A.) from June 18th till June 30th 1973. The In­ stitute was sponsored by NATO. Co-sponsors were: Agfa-Gevaert N.V. (Mortsel - Belgium), Bell Telephone Mfg. Co. (Antwerp­ Belgium), the National Science Foundation (Washington D.C. - U.S.A.) and the University of Antwerp (U.I.A.). A total of 120 lecturers and participants attended the Institute. Over the last few years, substantial progress has been made in the description of the elementary excitations of the elec­ tronic and vibrational systems and their interactions. Parallel with this, the experimentalists have obtained outstanding re­ sults, partly as a result of availability of coherent light sour­ ces from the far infrared through the visible region, and partly because of the availability of synchrotron radiation sources in the soft X-ray region. The results of today will lead to fur­ ther progress over the next years. It was the purpose of this NATO Advanced Study Institute to present astate of the art, namely a survey of experiment and theory.

Elementary Flight Dynamics with an Introduction to Bifurcation and Continuation Methods

Many textbooks are unable to step outside the classroom and connect with industrial practice, and most describe difficult-to-rationalize ad hoc derivations of the modal parameters. In contrast, Elementary Flight Dynamics with an Introduction to Bifurcation and Continuation Methods uses an optimal mix of physical insight and mathematical presentatio

Elementary Flight Dynamics with an Introduction to Bifurcation and Continuation Methods

Elementary Flight Dynamics with an Introduction to Bifurcation and Continuation Methods, Second Edition is aimed at senior undergraduate and graduate students of aerospace and mechanical engineering. The book uses an optimal mix of physical insight and mathematical presentation to illustrate the core concepts of professional aircraft flight dynamics. An updated version of the aerodynamic model is presented with the corrected definition of rate (dynamic) derivatives, supported with examples of real-life airplanes and related data and by open-source computational tools. It introduces bifurcation and continuation methods as a tool for flight dynamic analysis. FEATURES Covers an up-to-date, corrected, ‘clean’ presentation of the elements of flight dynamics Presents a blend of theory, practice and application with real-life practical examples Provides a unique viewpoint of applied aerodynamicists and aircraft designers Introduces bifurcation and continuation methods as a tool for flight dynamics analysis Includes a computational tool with real-life examples carried throughout the chapters The book is enriched with case studies of flight dynamics of a bird’s flight, of a six-seater rigid-wing airplane from a design perspective, and airship dynamics to highlight the modal behaviour of similar-looking vehicles that are distinct from each other. Excerpts from reviews of the first edition: "Flight dynamics is a topic that can cause difficulties to aerospace engineering students. This text leads the reader gently through the material with plenty of practical examples and student exercises. As such, it is easy to follow the material and to gradually develop a deep understanding of a demanding topic. The book is ideal for undergraduate students and is a good text for graduate students."––James F. Whidborne, Cranfield University, United Kingdom "The book covers all the aspects of flight dynamics traditionally found in such texts interspersed with examples of the treatment of features of current air vehicles....In my opinion, this book covers the subject comprehensively and is a desirable reference source for undergraduates and graduates alike."––R.J. Poole, MRAeS, The Aeronautical Journal, June 2014 "The book design and the methodology of interpretation are directed to a wide range of target audience/population interested in studying the dynamics of flight. Given the scale and organization of information, the book will also be a useful tool in the analysis of flight dynamics for professionals in this field. The book is sure to appeal to anyone interested in the dynamics of flight."––Jaroslav Salga, Advances in Military Technology, June 2014

Elementary Flight Dynamics with an Introduction to Bifurcation and Continuation Methods

Elementary Flight Dynamics with an Introduction to Bifurcation and Continuation Methods, Second Edition is aimed at senior undergraduate and graduate students of aerospace and mechanical engineering. The book uses an optimal mix of physical insight and mathematical presentation to illustrate the core concepts of professional aircraft flight dynamics. An updated version of the aerodynamic model is presented with the corrected definition of rate (dynamic) derivatives, supported with examples of real-life airplanes and related data and by open-source computational tools. It introduces bifurcation and continuation methods as a tool for flight dynamic analysis. FEATURES Covers an up-to-date, corrected, ‘clean’ presentation of the elements of flight dynamics Presents a blend of theory, practice and application with real-life practical examples Provides a unique viewpoint of applied aerodynamicists and aircraft designers Introduces bifurcation and continuation methods as a tool for flight dynamics analysis Includes a computational tool with real-life examples carried throughout the chapters The book is enriched with case studies of flight dynamics of a bird’s flight, of a six-seater rigid-wing airplane from a design perspective, and airship dynamics to highlight the modal behaviour of similar-looking vehicles that are distinct from each other. Excerpts from reviews of the first edition: "Flight dynamics is a topic that can cause difficulties to aerospace engineering students. This text leads the reader gently through the material with plenty of practical examples and student exercises. As such, it is easy to follow the material and to gradually develop a deep understanding of a demanding topic. The book is ideal for undergraduate students and is a good text for graduate students."––James F. Whidborne, Cranfield University, United Kingdom "The book covers all the aspects of flight dynamics traditionally found in such texts interspersed with examples of the treatment of features of current air vehicles....In my opinion, this book covers the subject comprehensively and is a desirable reference source for undergraduates and graduates alike."––R.J. Poole, MRAeS, The Aeronautical Journal, June 2014 "The book design and the methodology of interpretation are directed to a wide range of target audience/population interested in studying the dynamics of flight. Given the scale and organization of information, the book will also be a useful tool in the analysis of flight dynamics for professionals in this field. The book is sure to appeal to anyone interested in the dynamics of flight."––Jaroslav Salga, Advances in Military Technology, June 2014

Elementary Food Science (Food Science Text Series)

Following the success of the popular introductory text,Elementary Food Science(5th edition) coversabroad range of food science topics organized infour parts; Part (1)Interrelated food science topics, Part (2)Food safety & sanitation, Part (3)Food preservation and processing and Part (4)Handling & processing of foods. The opening two chapters discuss what food science actually is, the significanceforsociety, and the large contribution of the food industry to jobs and revenue in the USA and globally. Succeeding chapterscover food regulatory agencies, food labels, food quality and sensory evaluation, and consumer food literacy. Part (2)hastwo new chapters explaininghow microbes affect food quality,and alsofoodborne disease outbreaks; GMP is described independently and as a prerequisite for HACCP, VACCP andTACCPfood-safety management systems. Part (3) containstwo new chapters dealing with basic aspects of food processing, and the quality of dried foods. Part (4) covershandling and processing major food commodity groups (meat, dairy products, poultry and eggs, fish and shellfish, cereal grains, bakery products, fruits and vegetables, sugar confectionary). A new final chapter coversthe foodservice industry. The text highlights food science links with industry uniquelyusing the North American Industry Classification System (NAICS). Overall, the book is thoroughly modernized with over 1500 references cited in recognition of thousands of named food scientists and other professionals. The target readership remain unchanged for the current edition, i.e. Students of food science fromsenior high school, colleges or universities. Sections of the book will also appeal toadvanced readers from other disciplines with perhaps little or noprior food science experience. Additionally, readers covering the intersection of food science with culinary arts, foodservices, and nutritionor public health will find the book useful.

Elementary Food Science (Food Science Text Series)

Following the success of the previous editions, this popular introductory text continues to provide thorough, up-to-date information covering a broad range of topics in food science, with emphasis on food processing and handling and the methodology of specific foods. Presenting a multitude of easy-to-understand figures, tables, illustrated concepts and methods. This text maintains the strengths of the previous edition while adding new information. The book opens with a revised chapter on what food science actually is, detailing the progression of food science from beginning to future. Succeeding chapters include the latest information on food chemistry and dietary recommendations, food borne diseases and microbial activity. A complete revision of HACCP is outlined, accompanied by numerous examples of flow charts and applications, as well as major additions on food labeling. Extensive updates have been made on processing methods and handling of foods, such as new procedures on: candy making; coffee and tea production; beer and wine production; soft drinks; ultra high temperature processing; aseptic packaging; aquaculture and surimi; and UHT and low temperature pasteurization of milk. In addition, there is a completely new section which includes safety and sanitation as well as laboratory exercises in sensory, microbiological, chemical quality test, and processing methods for a variety of the foods described in previous chapters.

Elementary Introduction to Quantum Geometry

This graduate textbook provides an introduction to quantum gravity, when spacetime is two-dimensional. The quantization of gravity is the main missing piece of theoretical physics, but in two dimensions it can be done explicitly with elementary mathematical tools, but it still has most of the conceptional riddles present in higher dimensional (not yet known) quantum gravity. It provides an introduction to a very interdisciplinary field, uniting physics (quantum geometry) and mathematics (combinatorics) in a non-technical way, requiring no prior knowledge of quantum field theory or general relativity. Using the path integral, the chapters provide self-contained descriptions of random walks, random trees and random surfaces as statistical systems where the free relativistic particle, the relativistic bosonic string and two-dimensional quantum gravity are obtained as scaling limits at phase transition points of these statistical systems. The geometric nature of the theories allows one to perform the path integral by counting geometries. In this way the quantization of geometry becomes closely linked to the mathematical fields of combinatorics and probability theory. By counting the geometries, it is shown that the two-dimensional quantum world is fractal at all scales unless one imposes restrictions on the geometries. It is also discussed in simple terms how quantum geometry and quantum matter can interact strongly and change the properties both of the geometries and of the matter systems. It requires only basic undergraduate knowledge of classical mechanics, statistical mechanics and quantum mechanics, as well as some basic knowledge of mathematics at undergraduate level. It will be an ideal textbook for graduate students in theoretical and statistical physics and mathematics studying quantum gravity and quantum geometry. Key features: Presents the first elementary introduction to quantum geometry Explores how to understand quantum geometry without prior knowledge beyond bachelor level physics and mathematics. Contains exercises, problems and solutions to supplement and enhance learning

Elementary Introduction to Quantum Geometry

This graduate textbook provides an introduction to quantum gravity, when spacetime is two-dimensional. The quantization of gravity is the main missing piece of theoretical physics, but in two dimensions it can be done explicitly with elementary mathematical tools, but it still has most of the conceptional riddles present in higher dimensional (not yet known) quantum gravity. It provides an introduction to a very interdisciplinary field, uniting physics (quantum geometry) and mathematics (combinatorics) in a non-technical way, requiring no prior knowledge of quantum field theory or general relativity. Using the path integral, the chapters provide self-contained descriptions of random walks, random trees and random surfaces as statistical systems where the free relativistic particle, the relativistic bosonic string and two-dimensional quantum gravity are obtained as scaling limits at phase transition points of these statistical systems. The geometric nature of the theories allows one to perform the path integral by counting geometries. In this way the quantization of geometry becomes closely linked to the mathematical fields of combinatorics and probability theory. By counting the geometries, it is shown that the two-dimensional quantum world is fractal at all scales unless one imposes restrictions on the geometries. It is also discussed in simple terms how quantum geometry and quantum matter can interact strongly and change the properties both of the geometries and of the matter systems. It requires only basic undergraduate knowledge of classical mechanics, statistical mechanics and quantum mechanics, as well as some basic knowledge of mathematics at undergraduate level. It will be an ideal textbook for graduate students in theoretical and statistical physics and mathematics studying quantum gravity and quantum geometry. Key features: Presents the first elementary introduction to quantum geometry Explores how to understand quantum geometry without prior knowledge beyond bachelor level physics and mathematics. Contains exercises, problems and solutions to supplement and enhance learning