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Drawing on philosophical accounts of identity and individuality, as well as the histories of both classical and quantum physics, this book explores two alternative metaphysical approaches to quantum particles. It asks if quantum particles can be regarded as individuals, just like books, tables, and people. Taking the first approach, the book argues that if quantum particles are regarded as individuals, then Leibniz’s famous Principle of the Identity of Indiscernibles is in fact violated. Recent discussions of this conclusion are analysed in detail and the costs involved in saving the Principle are carefully considered. For the second approach, the book considers recent work in non-standard logic and set theory to indicate how we can make sense of the idea that objects can be non-individuals. The concluding chapter suggests how these results might then be extended to quantum field theory.

These nine chapters, commissioned on the initiative of the Philosophy section of the British Academy, address fundamental questions about time in philosophy, physics, linguistics, and psychology. Are there facts about the future? Could we affect the past? Physics, general relativity and quantum theory give contradictory treatments of time. So in the search for a theory of quantum gravity, which should give way: general relativity or quantum theory? In linguistics and psychology, how does our language represent time, and how do our minds keep track of it?

Do humans have a free choice of which actions to perform? Three recent developments of modern science can help us to answer this question. First, new investigative tools have enabled us to study the processes in our brains which accompanying our decisions. The pioneer work of Benjamin Libet has led many neuroscientists to hold the view that our conscious intentions do not cause our bodily movements but merely accompany them. Then, Quantum Theory suggests that not all physical events are fully determined by their causes, and so opens the possibility that not all brain events may be fully determined by their causes, and so maybe — if neuroscience does not rule this out — there is a role for intentions after all. Finally, a theorem of mathematics, Gödel's theory, has been interpreted to suggest that the initial conditions and laws of development of a mathematician's brain could not fully determine which mathematical conjectures he sees to be true. The extent to which human behaviour is determined by brain events may well depend on whether conscious events, such as intentions, are themselves merely brain events, or whether they are separate events which interact with brain events (perhaps in the radical form that intentions are events in our soul, and not in our body). This book considers what kind of free will we need in order to be morally responsible for our actions or be held guilty in a court of law. Is it sufficient merely that our actions are uncaused by brain events?

This book defends the view that the Everett interpretation of quantum theory, often called the ‘many worlds theory’, is not some new physical theory or some metaphysical addition to quantum theory, but simply quantum theory itself understood in a straightforwardly literal way. As such ‐ despite its radical implications for the nature of our universe ‐ the Everett interpretation is actually the conservative way to approach quantum theory, requiring revisions neither to our best theories of physics, nor to conventional philosophy of science. The book is in three parts. Part I explains how quantum theory implies the existence of an emergent branching structure in physical reality, and explores the conceptual and technical details of decoherence theory, the theory which allows us to quantify that branching. Part II is concerned with the problem of probability, and makes the case that probability, far from being the key difficulty for the Everett interpretation, actually makes more sense from a many‐worlds viewpoint. Part III explores the implications of an Everettian perspective on a variety of topics in physics and philosophy.

This book provides an introduction to the path integral formulation of quantum field theory and its applications to the analyses of symmetry breaking by the quantization procedure. This symmetry breaking is commonly called the ‘quantum anomaly’ or simply the ‘anomaly’, and this naming shows that the effect first appeared as an exceptional phenomenon in field theory. However, it is shown that this effect has turned out to be very fundamental in modern field theory. In the path integral formulation, it has been recognized that this effect arises from a non-trivial Jacobian in the change of path integral variables, namely, the path integral measure breaks certain symmetries. The study of the quantum anomaly attempts to bring about a better understanding of the basis of quantum theory and, consequently, it is a basic notion which could influence the entire quantum theory beyond field theory. The quantum anomaly is located at the border of divergence and convergence, though the quantum anomaly itself is perfectly finite, and thus closely related to the presence of an infinite number of degrees of freedom.

Quantum gravity is the name given to a theory that unites general relativity — Einstein's theory of gravitation and spacetime — with quantum field theory, our framework for describing non-gravitational forces. This book brings together philosophers and physicists to discuss a range of conceptual issues that surface in the effort to unite these theories, focusing in particular on the ontological nature of the spacetime that results. Although there has been a great deal written about quantum gravity from the perspective of physicists and mathematicians, very little attention has been paid to the philosophical aspects. This book closes that gap, with chapters written by some of the leading researchers in the field. Individual chapters defend or attack a structuralist perspective on the fundamental ontologies of our physical theories, which offers the possibility of shedding new light on a number of foundational problems.

This book is concerned with the attempts to unify Einstein's theory of general relativity and quantum theory into a theory of quantum gravity. It presents, for the first time, most of the approaches in a single textbook. Among them are canonical quantum gravity (including loop quantum gravity), covariant quantum gravity, and string theory. The book also discusses the relevance of these theories for cosmology and the physics of black holes. The first chapter gives a general introduction to the problem of quantizing the gravitational field. The second chapter then presents the main covariant approaches - perturbation theory and Feynman diagrammes, path integrals, and supergravity. The third chapter discusses the important concept of reparametrization invariance in the framework of simple systems: particle models, bosonic string, and parametrized field theory. This concept plays a crucial role in the Hamiltonian formulation of general relativity, which is the topic of Chapter 4. Chapter 5 presents the canonical quantization in the metric variables, leading to the central Wheeler-DeWitt equation, while the sixth chapter presents loop quantum gravity. The next two chapters 7 and 8 then discuss the major applications - quantization of black holes and quantum cosmology. Chapter 9 gives an introduction to string theory by focusing on its quantum gravitational aspects. Chapter 10 contains a discussion of interpretational issues: the relevance of quantum gravity for the foundations of quantum theory and the arrow of time. It also contains a brief review of quantum-gravity phenomenology. The emphasis throughout is on conceptual and formal clarity. Wherever possible, connections between the various approaches are examined.

The book opens with a chapter on the classical theory of multipoles in electromagnetism, in which static and dynamic multipole expansions of various physical quantities are derived, including of the Maxwell fields D and H. Chapter 2 presents a semi-classical account of multipole theory, in which the Barron-Gray gauge is used to derive multipole polarizabilities describing the induction of molecular moments by a harmonic plane wave. Aspects of symmetry are treated in Chapter 3 — space-time behaviour of tensors and physical properties of molecules and crystals. In Chapter 4, D(E,B) and H(E,B) are obtained for linear anisotropic media, yielding expressions for the material constants which are required to satisfy origin independence, the Post constraint, and certain symmetries but fail the first two. Despite these difficulties, the standard theory is used in Chapter 5 to derive a wave propagation equation; this is applied to explain various physical effects in transmission, two of which are also described in a scattering theory. Chapter 6 deals with the reflection of electromagnetic waves from an anisotropic medium. The reflected intensities violate origin independence, showing again the unphysical nature of existing multipole theory. In Chapter 7, the fields are transformed while leaving Maxwell's equations unchanged, from which new material constants are derived in Chapter 8 that meet the three requirements in Chapter 4. Chapter 9 applies the transformed expressions to transmission and reflection phenomena, confirming the results of Chapter 5, while yielding reflected intensities that satisfy space and time invariances.

For most of the last century, condensed matter physics has been dominated by band theory and Landau's symmetry breaking theory. In the last twenty years, however, there has been an emergence of a new paradigm associated with fractionalization, emergent gauge bosons and fermions, topological order, string-net condensation, and long range entanglements. These new physical concepts are so fundamental that they may even influence our understanding of the origin of light and electrons in the universe. This book is a pedagogical and systematic introduction to the new concepts and quantum field theoretical methods in condensed matter physics. It discusses many basic notions in theoretical physics which underlie physical phenomena in nature, including a notion that unifies light and electrons. Topics covered include dissipative quantum systems, boson condensation, symmetry breaking and gapless excitations, phase transitions, Fermi liquids, spin density wave states, Fermi and fractional statistics, quantum Hall effects, topological/quantum order, and spin liquid and string-net condensation. Methods discussed include the path integral, Green's functions, mean-field theory, effective theory, renormalization group, bosonization in one- and higher dimensions, non-linear sigma-model, quantum gauge theory, dualities, projective construction, and exactly soluble models beyond one-dimension.

This book develops the quantum theory of solids from the basic principles of quantum mechanics. The emphasis is on a single statement of the ideas underlying the various approximations that have to be used in the study of this subject. Care is taken to separate sound arguments from conjecture. The treatment covers the electron theory of metals as well as the dynamics of crystals, including the author's work on the thermal conductivity of crystals.