Gauge Fields, Knots And Gravity by Baez/Muniain

[ibkev]

I'm curious about John Baez's book "Gauge Fields, Knots And Gravity" - I've read some of notes from his website and find his style of writing well matched to my style of learning. So, for personal interest, I was considering whether this book might be nice to read.

That said, I'm not familiar with knot theory at all and was wondering if there is a simple way to describe the "big idea" and where it fits into modern physics?

 

[Greg Bernhardt]

Paging @john baez

 

[john baez]

Yes, the book is nice to read. It teaches you the basics of differential geometry and how this math shows up in the fundamental laws of physics: special relativity, Maxwell's equations, the Yang-Mills equations and general relativity. It also introduces the basic ideas of knot theory and shows how knot theory is connected to Chern-Simons theory (a field theory with certain relationships to general relativity). It then sketches the basics of loop quantum gravity and how it's related to knot theory and Chern-Simons theory.

Someday I would like to write a modified version of this book which eliminates all the knot theory and loop quantum gravity, and says more about differential geometry, special relativity, Maxwell's equations, the Yang-Mills equations and general relativity. That would be a more conservative book, written by an older and wiser man.

 

[ibkev]

That sounds pretty cool actually - thanks for replying! Out of curiosity, now that you are an older and wiser man do you think knot theory and LQG still hold the same promise that you once did (which, I assume, is why they are covered in the book)?

 

[john baez]

No, I'm no longer optimistic that anyone will figure out quantum gravity anytime soon. That's why I quit working on it over a decade ago. For more:

• What have you changed your mind about: Should I be thinking about quantum gravity?

 

[Demystifier]

• What have you changed your mind about: Should I be thinking about quantum gravity?

This great essay is a part of a great book https://www.amazon.com/dp/0061686549/?tag=pfamazon01-20 . And it reminds me of my own essay https://www.physicsforums.com/insights/stopped-worrying-learned-love-orthodox-quantum-mechanics/

 

[jakob1111]

I'm curious about John Baez's book "Gauge Fields, Knots And Gravity" - I've read some of notes from his website and find his style of writing well matched to my style of learning. So, for personal interest, I was considering whether this book might be nice to read.

That said, I'm not familiar with knot theory at all and was wondering if there is a simple way to describe the "big idea" and where it fits into modern physics?

The book is amazing. If you get stuck somewhere, I recommend having a look at the http://michaelnielsen.org/blog/yang_mills.pdfn. His alternative formulations often help to understand things better.

 

[ibkev]

My original post was in part about getting some idea what knot theory might relate/apply to, so for others interested in the same thing here’s an article by Nobel winning physicist Frank Wilczek about how knots and quantum statistics may predict a new particle!

https://www.quantamagazine.org/how-anyon-particles-emerge-from-quantum-knots-20170228/