Elementary Introduction to Quantum Geometry is popular PDF and ePub book, written by Jan Ambjorn in 2022-11-02, it is a fantastic choice for those who relish reading online the Science genre. Let's immerse ourselves in this engaging Science book by exploring the summary and details provided below. Remember, Elementary Introduction to Quantum Geometry can be Read Online from any device for your convenience.
Elementary Introduction to Quantum Geometry Book PDF Summary
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
Detail Book of Elementary Introduction to Quantum Geometry PDF
- Author : Jan Ambjorn
- Release : 02 November 2022
- Publisher : CRC Press
- ISBN : 9781000776027
- Genre : Science
- Total Page : 329 pages
- Language : English
- PDF File Size : 11,9 Mb
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