This volume provides a self-contained introduction to applications of loop representations, and the related topic of knot theory, in particle physics and quantum gravity. These topics are of considerable interest because they provide a unified arena for the study of the gauge invariant quantization of Yang-Mills theories and gravity, and suggest a promising approach to the eventual unification of the four fundamental forces. The book begins with a detailed review of loop representation theory and then describes loop representations in Maxwell theory, Yang-Mills theories as well as lattice techniques. Applications in quantum gravity are then discussed, with the following chapters considering knot theories, braid theories and extended loop representations in quantum gravity. A final chapter assesses the current status of the theory and points out possible directions for future research. First published in 1996, this title has been reissued as an Open Access publication on Cambridge Core.

This volume provides a self-contained introduction to applications of loop representations, and the related topic of knot theory, in particle physics and quantum gravity. These topics are of considerable interest because they provide a unified arena for the study of the gauge invariant quantization of Yang-Mills theories and gravity, and suggest a promising approach to the eventual unification of the four fundamental forces. The book begins with a detailed review of loop representation theory and then describes loop representations in Maxwell theory, Yang-Mills theories as well as lattice techniques. Applications in quantum gravity are then discussed, with the following chapters considering knot theories, braid theories and extended loop representations in quantum gravity. A final chapter assesses the current status of the theory and points out possible directions for future research. First published in 1996, this title has been reissued as an Open Access publication on Cambridge Core.

This book provides an accessible introduction to loop quantum gravity and some of its applications, at a level suitable for undergraduate students and others with only a minimal knowledge of college level physics. In particular it is not assumed that the reader is familiar with general relativity and only minimally familiar with quantum mechanics and Hamiltonian mechanics. Most chapters end with problems that elaborate on the text, and aid learning. Applications such as loop quantum cosmology, black hole entropy and spin foams are briefly covered. The text is ideally suited for an undergraduate course in the senior year of a physics major. It can also be used to introduce undergraduates to general relativity and quantum field theory as part of a 'special topics' type of course.
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What is consciousness? Does free will exist?There exists a widespread conviction that the recent scientific discoveries, especially those related to physics and biology, in particular in contemporary neurosciences, question the traditional attempts to give meaning to life and a basis for our moral compass. Current scientific thinking usually identifies the mind with the mere exchange of electrical signals among neurons. It claims that consciousness is an irrelevant epiphenomenon and that introspection is an unreliable instrument to achieve any form of knowledge. Also, that the physical universe is causally closed and therefore all that occurs only has physical causes and all kind of freedom is excluded. The problem of assigning meaning and purpose to our lives, to the essential conceptions of the value of human life and social justice, becomes practically insoluble if one accepts the predominant notions that supposedly stem from contemporary science. The clash between the scientific and humanistic conception of human beings seems to have no option but to abandon the latter.The aim of this book is to show that, contrary to what is usually considered, current advances in science allow to re-evaluate the role of consciousness and human freedom without entering into contradiction with empirical evidence or scientific theories in place today. The book starts by analyzing the certainties provided by the scientific thought and philosophical reflection while discussing the role and content of physical theories, and in particular, quantum mechanics. It discusses in detail the nature of quantum objects and the role they may have in consciousness. In particular, it analyzes models that allow phenomena of quantum nature to manifest themselves in the brains of animals and humans, and account for many of the properties of consciousness. Finally, we analyze how self-conscious and free entities like persons emerge, making compatible the scientific view with a renewed and better supported way of perceiving people, their values and culture.