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Author: Jim Baggott
Publisher: Oxford University Press
ISBN: 019253680X
Category : Science
Languages : en
Pages : 320
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Book Description
Today we are blessed with two extraordinarily successful theories of physics. The first is Albert Einstein's general theory of relativity, which describes the large-scale behaviour of matter in a curved spacetime. This theory is the basis for the standard model of big bang cosmology. The discovery of gravitational waves at the LIGO observatory in the US (and then Virgo, in Italy) is only the most recent of this theory's many triumphs. The second is quantum mechanics. This theory describes the properties and behaviour of matter and radiation at their smallest scales. It is the basis for the standard model of particle physics, which builds up all the visible constituents of the universe out of collections of quarks, electrons and force-carrying particles such as photons. The discovery of the Higgs boson at CERN in Geneva is only the most recent of this theory's many triumphs. But, while they are both highly successful, these two structures leave a lot of important questions unanswered. They are also based on two different interpretations of space and time, and are therefore fundamentally incompatible. We have two descriptions but, as far as we know, we've only ever had one universe. What we need is a quantum theory of gravity. Approaches to formulating such a theory have primarily followed two paths. One leads to String Theory, which has for long been fashionable, and about which much has been written. But String Theory has become mired in problems. In this book, Jim Baggott describes ": an approach which takes relativity as its starting point, and leads to a structure called Loop Quantum Gravity. Baggott tells the story through the careers and pioneering work of two of the theory's most prominent contributors, Lee Smolin and Carlo Rovelli. Combining clear discussions of both quantum theory and general relativity, this book offers one of the first efforts to explain the new quantum theory of space and time.
Author: Jim Baggott
Publisher: Oxford University Press
ISBN: 019253680X
Category : Science
Languages : en
Pages : 320
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Book Description
Today we are blessed with two extraordinarily successful theories of physics. The first is Albert Einstein's general theory of relativity, which describes the large-scale behaviour of matter in a curved spacetime. This theory is the basis for the standard model of big bang cosmology. The discovery of gravitational waves at the LIGO observatory in the US (and then Virgo, in Italy) is only the most recent of this theory's many triumphs. The second is quantum mechanics. This theory describes the properties and behaviour of matter and radiation at their smallest scales. It is the basis for the standard model of particle physics, which builds up all the visible constituents of the universe out of collections of quarks, electrons and force-carrying particles such as photons. The discovery of the Higgs boson at CERN in Geneva is only the most recent of this theory's many triumphs. But, while they are both highly successful, these two structures leave a lot of important questions unanswered. They are also based on two different interpretations of space and time, and are therefore fundamentally incompatible. We have two descriptions but, as far as we know, we've only ever had one universe. What we need is a quantum theory of gravity. Approaches to formulating such a theory have primarily followed two paths. One leads to String Theory, which has for long been fashionable, and about which much has been written. But String Theory has become mired in problems. In this book, Jim Baggott describes ": an approach which takes relativity as its starting point, and leads to a structure called Loop Quantum Gravity. Baggott tells the story through the careers and pioneering work of two of the theory's most prominent contributors, Lee Smolin and Carlo Rovelli. Combining clear discussions of both quantum theory and general relativity, this book offers one of the first efforts to explain the new quantum theory of space and time.
Author: Vincent Rivasseau
Publisher: Springer Science & Business Media
ISBN: 3764385227
Category : Science
Languages : en
Pages : 228
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Book Description
This book confirms noncommutative geometry as an increasingly useful tool for the description of intricate condensed matter phenomena. It describes the striking progress recently made in gathering all the interactions and fields of the standard model into a non-commutative geometry on a simple internal space. Coverage also details the very recent technique of renormalization of quantum field theories on non-commutative space-time.
Author: David W. Cohen
Publisher: Springer Science & Business Media
ISBN: 1461388414
Category : Science
Languages : en
Pages : 159
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Book Description
Historically, nonclassical physics developed in three stages. First came a collection of ad hoc assumptions and then a cookbook of equations known as "quantum mechanics". The equations and their philosophical underpinnings were then collected into a model based on the mathematics of Hilbert space. From the Hilbert space model came the abstaction of "quantum logics". This book explores all three stages, but not in historical order. Instead, in an effort to illustrate how physics and abstract mathematics influence each other we hop back and forth between a purely mathematical development of Hilbert space, and a physically motivated definition of a logic, partially linking the two throughout, and then bringing them together at the deepest level in the last two chapters. This book should be accessible to undergraduate and beginning graduate students in both mathematics and physics. The only strict prerequisites are calculus and linear algebra, but the level of mathematical sophistication assumes at least one or two intermediate courses, for example in mathematical analysis or advanced calculus. No background in physics is assumed.
Author: Wolfgang P. Schleich
Publisher: John Wiley & Sons
ISBN: 352780255X
Category : Science
Languages : en
Pages : 723
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Book Description
Quantum Optics in Phase Space provides a concise introduction to the rapidly moving field of quantum optics from the point of view of phase space. Modern in style and didactically skillful, Quantum Optics in Phase Space prepares students for their own research by presenting detailed derivations, many illustrations and a large set of workable problems at the end of each chapter. Often, the theoretical treatments are accompanied by the corresponding experiments. An exhaustive list of references provides a guide to the literature. Quantum Optics in Phase Space also serves advanced researchers as a comprehensive reference book. Starting with an extensive review of the experiments that define quantum optics and a brief summary of the foundations of quantum mechanics the author Wolfgang P. Schleich illustrates the properties of quantum states with the help of the Wigner phase space distribution function. His description of waves ala WKB connects semi-classical phase space with the Berry phase. These semi-classical techniques provide deeper insight into the timely topics of wave packet dynamics, fractional revivals and the Talbot effect. Whereas the first half of the book deals with mechanical oscillators such as ions in a trap or atoms in a standing wave the second half addresses problems where the quantization of the radiation field is of importance. Such topics extensively discussed include optical interferometry, the atom-field interaction, quantum state preparation and measurement, entanglement, decoherence, the one-atom maser and atom optics in quantized light fields. Quantum Optics in Phase Space presents the subject of quantum optics as transparently as possible. Giving wide-ranging references, it enables students to study and solve problems with modern scientific literature. The result is a remarkably concise yet comprehensive and accessible text- and reference book - an inspiring source of information and insight for students, teachers and researchers alike.
Author: N. D. Birrell
Publisher: Cambridge University Press
ISBN: 1107392810
Category : Science
Languages : en
Pages : 362
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Book Description
This book presents a comprehensive review of the subject of gravitational effects in quantum field theory. Although the treatment is general, special emphasis is given to the Hawking black hole evaporation effect, and to particle creation processes in the early universe. The last decade has witnessed a phenomenal growth in this subject. This is the first attempt to collect and unify the vast literature that has contributed to this development. All the major technical results are presented, and the theory is developed carefully from first principles. Here is everything that students or researchers will need to embark upon calculations involving quantum effects of gravity at the so-called one-loop approximation level.
Author: Asao Arai
Publisher: World Scientific
ISBN: 9813207132
Category : Science
Languages : en
Pages : 893
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Book Description
This book provides a comprehensive introduction to Fock space theory and its applications to mathematical quantum field theory. The first half of the book, Part I, is devoted to detailed descriptions of analysis on abstract Fock spaces (full Fock space, boson Fock space, fermion Fock space and boson-fermion Fock space). It includes the mathematics of second quantization, representation theory of canonical commutation relations and canonical anti-commutation relations, Bogoliubov transformations, infinite-dimensional Dirac operators and supersymmetric quantum field in an abstract form. The second half of the book, Part II, covers applications of the mathematical theories in Part I to quantum field theory. Four kinds of free quantum fields are constructed and detailed analyses are made. A simple interacting quantum field model, called the van Hove model, is fully analyzed in an abstract form. Moreover, a list of interacting quantum field models is presented and a short description to each model is given.To graduate students in mathematics or physics who are interested in the mathematical aspects of quantum field theory, this book is a good introductory text. It is also well suited for self-study and will provide readers a firm foundation of knowledge and mathematical techniques for reading more advanced books and current research articles in the field of mathematical analysis on quantum fields. Also, numerous problems are added to aid readers to develop a deeper understanding of the field.
Author: W.-H. Steeb
Publisher: Springer Science & Business Media
ISBN: 9401153329
Category : Science
Languages : en
Pages : 247
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Book Description
This book gives a comprehensive introduction to modern quantum mechanics, emphasising the underlying Hilbert space theory and generalised function theory. All the major modern techniques and approaches used in quantum mechanics are introduced, such as Berry phase, coherent and squeezed states, quantum computing, solitons and quantum mechanics. Audience: The book is suitable for graduate students in physics and mathematics.
Author: Cosmas Zachos
Publisher: World Scientific
ISBN: 9812383840
Category : Science
Languages : en
Pages : 560
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Book Description
Wigner's quasi-probability distribution function in phase space is a special (Weyl) representation of the density matrix. It has been useful in describing quantum transport in quantum optics; nuclear physics; decoherence, quantum computing, and quantum chaos. It is also important in signal processing and the mathematics of algebraic deformation. A remarkable aspect of its internal logic, pioneered by Groenewold and Moyal, has only emerged in the last quarter-century: it furnishes a third, alternative, formulation of quantum mechanics, independent of the conventional Hilbert space, or path integral formulations.In this logically complete and self-standing formulation, one need not choose sides ? coordinate or momentum space. It works in full phase space, accommodating the uncertainty principle, and it offers unique insights into the classical limit of quantum theory. This invaluable book is a collection of the seminal papers on the formulation, with an introductory overview which provides a trail map for those papers; an extensive bibliography; and simple illustrations, suitable for applications to a broad range of physics problems. It can provide supplementary material for a beginning graduate course in quantum mechanics.
Author: Brian C. Hall
Publisher: Springer Science & Business Media
ISBN: 1461471168
Category : Science
Languages : en
Pages : 566
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Book Description
Although ideas from quantum physics play an important role in many parts of modern mathematics, there are few books about quantum mechanics aimed at mathematicians. This book introduces the main ideas of quantum mechanics in language familiar to mathematicians. Readers with little prior exposure to physics will enjoy the book's conversational tone as they delve into such topics as the Hilbert space approach to quantum theory; the Schrödinger equation in one space dimension; the Spectral Theorem for bounded and unbounded self-adjoint operators; the Stone–von Neumann Theorem; the Wentzel–Kramers–Brillouin approximation; the role of Lie groups and Lie algebras in quantum mechanics; and the path-integral approach to quantum mechanics. The numerous exercises at the end of each chapter make the book suitable for both graduate courses and independent study. Most of the text is accessible to graduate students in mathematics who have had a first course in real analysis, covering the basics of L2 spaces and Hilbert spaces. The final chapters introduce readers who are familiar with the theory of manifolds to more advanced topics, including geometric quantization.
Author: Eduard Prugovečki
Publisher: Springer Science & Business Media
ISBN: 9789027716170
Category : Gardening
Languages : en
Pages : 334
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Book Description
The principal intent of this monograph is to present in a systematic and self-con tained fashion the basic tenets, ideas and results of a framework for the consistent unification of relativity and quantum theory based on a quantum concept of spacetime, and incorporating the basic principles of the theory of stochastic spaces in combination with those of Born's reciprocity theory. In this context, by the physicial consistency of the present framework we mean that the advocated approach to relativistic quantum theory relies on a consistent probabilistic interpretation, which is proven to be a direct extrapolation of the conventional interpretation of nonrelativistic quantum mechanics. The central issue here is that we can derive conserved and relativistically convariant probability currents, which are shown to merge into their nonrelativistic counterparts in the nonrelativistic limit, and which at the same time explain the physical and mathe matical reasons behind the basic fact that no probability currents that consistently describe pointlike particle localizability exist in conventional relativistic quantum mechanics. Thus, it is not that we dispense with the concept oflocality, but rather the advanced central thesis is that the classical concept of locality based on point like localizability is inconsistent in the realm of relativistic quantum theory, and should be replaced by a concept of quantum locality based on stochastically formulated systems of covariance and related to the aforementioned currents.
