Category theory and beyond the standard model

[CarlB]

I've sometimes found that exhibiting just a touch of madness helps when dealing with the government and other authorities, depending on the effect desired. For example, explaining that Einstein was wrong, you've found the unified field theory, and are working on it at home does wonders.

 

[CarlB]

I need to find a way to include 'naive' in my tag line. Isn't symmetry breaking merely a geometric extension of relativity? I like the geometry part and can see how you can derive relavativistic reference frames in any coordinate system. But, symmetry breaking, as conventionally portrayed, appears suspect. Symmetries merely converge, IMO.

I don't believe in symmetry breaking, but I'm having trouble figuring out the rest of your post. How is symmetry breaking a geometric extension of relativity? One is in QM, the other GR, and they're not combined. And what does "Symmetries must converge" mean in more detail?

 

[arivero]

Aww, I wish I could have taken a category theory course when I was a teenage undergraduate. (Or even have heard of it!)

Well, there is not yet undergraduate category for physicists, but mathematicians are a lot more conversant on it than ten years before.

the next buzzword is "scheme"

 

[George Jones]

Well, there is not yet undergraduate category for physicists, but mathematicians are a lot more conversant on it than ten years before.

But there is! At least in book form - https://www.amazon.com/gp/product/0226288625/?tag=pfamazon01-20, by Robert Geroch. Geroch purposely and provocatively chose his title to indicate that, these days, mathematical physics includes topics other than those covered in more traditional mathematical physics courses. He starts with a few pages on category theory and and uses category theory as framework for discussing many topics.

Geroch's book contains a broad survey of abstract algebra, topology, and functional analysis, and it does a wonderful job at motivating (mathematically) mathematical definitions and constructions. However, its layout is abominable. Surprisingly, since Geroch is an expert, it contains no differential geometry.

This book was first published over twenty years ago, and is based on a course Geroch gave at the University of Chicago.

 

[Kea]

This book was first published over twenty years ago, and is based on a course Geroch gave at the University of Chicago.

Yeah, cool. Of course, being at Chicago (one of the founding centres of Category Theory) one would find it difficult to escape categories.

 

[CarlB]

Lubos got a little interested in Centauros:
http://motls.blogspot.com/2007/01/centauro-events-and-small-black-holes.html

 

[Kea]

Lubos got a little interested in Centauros...

Goodness knows why. It's hard to imagine he's thinking what you're thinking ...

 

[CarlB]

Oh no, it's just clear that cosmic rays are where the next new physics comes from, if it's not the LHC.

 

[Kea]

...it's just clear that cosmic rays are where the next new physics comes from, if it's not the LHC.

Well, there's a whole host of exciting possibilities. They just spotted a black hole at the centre of a globular cluster - only the second one they looked at.

 

[CarlB]

I would think that finding a black hole in the center of a globular cluster would put new wind under the MOND sails. By the way, I just realized that when I wrote "new physics", being a particle guy, I automatically meant new particle physics, and was thinking in terms of detectors rather than obesrvatories.