This is an introduction to the basic tools of mathematics needed to understand the relation between knot theory and quantum gravity. The book begins with a. Title, Gauge Fields, Knots and Gravity Volume 4 of K & E series on knots and everything. Author, John C. Baez. Edition, reprint. Publisher, World Scientific, Gauge Fields, Knots and Gravity has 44 ratings and 3 reviews. Jon said: This text is aimed at undergraduates, but I would readily recommend it to grad st.
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Description This is an introduction to the basic tools of mathematics needed to understand the relation between knot theory and quantum gravity. The book begins with a rapid course on manifolds jihn differential forms, emphasizing how these provide a proper language for formulating Maxwell’s equations on arbitrary spacetimes. The authors then introduce vector bundles, connections and curvature in order to generalize Maxwell theory to the Yang-Mills equations.
The relation of gauge theory to the newly discovered knot invariants such as the Gravuty polynomial is sketched. Riemannian geometry is then introduced in order to describe Einstein’s equations of general relativity and show how an attempt to quantize gravity leads to interesting applications of knot theory.
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Backgrounds Of Arithmetic And Geometry: Chaotic Dynamics In Hamiltonian Systems: From Order To Chaos – Essays: Critical, Chaotic And Otherwise: Table of contents Electromagnetism: Review quote “This book is a great introduction to many of the modern ideas of mathematical physics including foelds geometry, group theory, knot theory and topology.
It uses as ‘physical excuses’ to introduce these gaugd Maxwell theory, Yang-Mills theories and general relativity including its Ashtekar reformulation. The style of the book is quite lively and explanations are very clear.
Gauge Fields, Knots And Gravity
The treatment is mathematically and physically self-contained It offers an excellent way of treating the baeez with mathematical rigor while keeping the physical motivation and usefulness of these mathematical concepts close at hand.
For the individual reader, it is a great way to be lured into the study of the mathematics that underlies contemporary theoretical physics.
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