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A First Course in Loop Quantum Gravity
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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183 pages, Hardcover
First published January 1, 2011
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July 11, 2026
This book is bursting with ideas. High school physics is not an adequate basis. I am familiar with General Relativity, Lagrangians and Hamiltonians, Schrödinger's equation, second order quantisation and Fourier Transforms: even that was barely enough. But I did learn how to introduce constraints into Lagrangians and Hamiltonians, so that was worth the price of admission.
So a big problem for Quantum Gravity is the fact that there is a priori no coordinate system we can use, and trying to build one is next to impossible. So instead we assume a network of vertices, links and faces in three dimensions. For any loop, we can add up the properties of all links that pass through the loop. For any polyhedron, we can add up the properties of all the vertices that lie within it. This is closer to topology and finite mathematics than to any continuous structure. But that's the point. We have calculable functions without coordinates: a sort of proto-calculus, with very powerful symmetries.
So a big problem for Quantum Gravity is the fact that there is a priori no coordinate system we can use, and trying to build one is next to impossible. So instead we assume a network of vertices, links and faces in three dimensions. For any loop, we can add up the properties of all links that pass through the loop. For any polyhedron, we can add up the properties of all the vertices that lie within it. This is closer to topology and finite mathematics than to any continuous structure. But that's the point. We have calculable functions without coordinates: a sort of proto-calculus, with very powerful symmetries.
Displaying 1 of 1 review