The Geometry and Physics of Knots (Lezioni Lincee) 1st Edition by Michael Atiyah (PDF)

Description

These notes arise from lectures presented in Florence under the auspices of the Accadamia dei Lincee and deal with an area that lies at the crossroads of mathematics and physics. The material presented here rests primarily on the pioneering work of Vaughan Jones and Edward Witten relating polynomial invariants of knots to a topological quantum field theory in 2+1 dimensions. Professor Atiyah here presents an introduction to Witten’s ideas from the mathematical point of view. The book will be essential reading for all geometers and gauge theorists as an exposition of new and interesting ideas in a rapidly developing area.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is not a detailed treatise on quantum field theory and knot invariants. Mathematical details are kept to minimum and the overall exposition is terse, but readers with prior exposure to this topic can find it a useful read.

⭐It is a very helpful and useful book and a pretty good deal. I can learn a lot through this book.

⭐This book is a very quick overview of what was known at the time (1989) about the connection between quantum field theory and knot theory. The subject of topological quantum field theories and their connection with knot invariants was at that time just beginning thanks to the work of Edward Witten on the Jones polynomial. The approach that the author takes in the book is very formal and not for the beginner who is looking to learn about these results. Readers with enough background to read it will no doubt want to read more up-to-date treatments of the subject. The book however does give an indication of how Feynman path integrals are used to define the invariants. The use of these is not rigorous mathematics and this has not changed at the present day.

⭐well done

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