Gauge fields, knots, and gravity
by John C. Baez · first published 1994
67% recommend33% neutral
Why HN recommends it
Cheap, fairly accessible introduction to applications of topology in mathematical physics, with the geometric formulation of gauge theory covered in part 1 and exercises included; suits readers with a physics background.
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I haven't fully worked through it yet, but I've been really enjoying reading John Baez's Gauge Fields, Knots, and Gravity [1]. [1]: http://www.worldscientific.com/worldscibooks/10.1142/2324
on “So You Want to Learn Physics” ↗…Spivak's 'Calculus on Manifolds' but this never really did it for me. If you have a background in physics then some combination of Nakahara's 'Geometry, Topology and Physics' and Baez and Muniain's 'Gauge Fields, Knots and Gravity' might be good (I haven't included relativity textbooks as I assume it you have a background in GR then you have enough differential geometry). An unusual recommendation that I think is really nice is…
on “Learning Math for Machine Learning” ↗…following texts to a larger extent than others: - Algebra: Chapter 0 (Aluffi) - Real Mathematical Analysis (Pugh) - Mathematics and its History (Stillwell) - An Introduction to Manifolds (Tu) - Gauge Fields, Knots and Gravity (Baez) - A First Look at Rigorous Probability Theory (Rosenthal) - All of Statistics (Wasserman) There are some authors I trust and am happy to buy so long as the topic vaguely interests me: VI Arnold,…
on “Ask HN: Math books that made you significantly better at math?” ↗One of the authors, Baez, wrote "Gauge Fields, Knots, and Gravity" a lovely, cheap, and fairly accessible intro to applications of topology in mathematical physics. Worth a glance if you find yourself wondering about all this
on “Physics, Topology, Logic and Computation: A Rosetta Stone” ↗I think the idea of knots as a basis for everything has come and gone several times. One of those were in the 90s, which is when I became aware thanks to the excellent "Gauge Fields, Knots and Gravity" by John Baez and Javier P Muniain, that was part of the "Series on Knots and Everything" [1]. Those are really intriguing ideas. [1] https://www.worldscientific.com/series/skae
on “A “knot dominated era” may have existed in the early universe: study” ↗If you do want to learn the geometric formulation, part 1 of Gauge Fields, Knots and Gravity is a good resource (and has exercises!).
on “Why is Maxwell's theory so hard to understand? (2007) [pdf]” ↗it's more that they're built on differential forms and the exterior derivative. for a reference, see section 4.6 and problem 19.13 of an introduction to manifolds by loring tu. this is also covered in gauge fields, knots and gravity by baez and muniain and in much detail in foundations of classical electrodynamics by hehl and obukhov.
on “Seven-Dimensional Cross Product” ↗I wrote "Gauge Fields, Knots and Gravity", but we were talking about my uncle, who wrote "The New College Physics: a Spiral Approach".
on “How I Learned to Love Algebraic Geometry” ↗Wow I never look at usernames but maybe I should start. I believe I read his `Gauge Fields, Knots, and Gravity` back in college (or tried to, anyways. it was a touch above my level at the time)
on “If gravity isn't a force, then why does it "need" a boson?” ↗