Insights Higher Prequantum Geometry I: The Need for Prequantum Geometry - Comments

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I really like your posts. Extremely interesting. Thank you very much!
 

john baez

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A really nice introduction! A few typos:

behoves |-> behooves

two bad line breaks:

More generally, p-brane charges are not quantized in ordinary integral cohomology, but in generalized cohomology theories.
For instance 1-branes

and

homotopy 0-types —
are generalized to homotopy p-types
 

WWGD

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A really nice introduction! A few typos:

behoves |-> behooves

two bad line breaks:

More generally, p-brane charges are not quantized in ordinary integral cohomology, but in generalized cohomology theories.
For instance 1-branes

and

homotopy 0-types —
are generalized to homotopy p-types
Who are you calling a p-brane?
 

Urs Schreiber

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A really nice introduction! A few typos:

behoves |-> behooves

two bad line breaks:

More generally, p-brane charges are not quantized in ordinary integral cohomology, but in generalized cohomology theories.
For instance 1-branes

and

homotopy 0-types —
are generalized to homotopy p-types
Thanks! Fixed now.
 

Urs Schreiber

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A really nice introduction! A few typos:

behoves |-> behooves

two bad line breaks:

More generally, p-brane charges are not quantized in ordinary integral cohomology, but in generalized cohomology theories.
For instance 1-branes

and

homotopy 0-types —
are generalized to homotopy p-types
Who are you calling a p-brane?
Urs says:

At least on my system there is some odd effect with the comment citations not coming out properly. I have added above some white space such as to hopefully make it discernible who is speaking now.

This here in reply to the question "Who are you calling a p-brane?"

The super-p-branes that I am speaking about are precisely those famous from string/M-theory. I have talked about these from a perspective that will be relevant for the present dicussion earlier in the article "Emergence form the superpoint" https://www.physicsforums.com/insights/emergence-from-the-superpoint/ . In two or three further installments here we will see how it all comes together and how the higher prequantization of super-p-branes works and what it tellsus about brane charge quantization conditions in string/M-theory.
 
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This here in reply to the question "Who are you calling a p-brane?"

The super-p-branes that I am speaking about are precisely those famous from string/M-theory. I have talked about these from a perspective that will be relevant for the present dicussion earlier in the article "Emergence form the superpoint" https://www.physicsforums.com/insights/emergence-from-the-superpoint/ . In two or three further installments here we will see how it all comes together and how the higher prequantization of super-p-branes works and what it tellsus about brane charge quantization conditions in string/M-theory.
I think you missed the homophone WWGD alluded at, p-brane sounds like a peabrain

on-topic, I only skimmed the article for now. Its a "little" over my head at this time.
It looked really nice though.
 

WWGD

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Urs says:

At least on my system there is some odd effect with the comment citations not coming out properly. I have added above some white space such as to hopefully make it discernible who is speaking now.

This here in reply to the question "Who are you calling a p-brane?"

The super-p-branes that I am speaking about are precisely those famous from string/M-theory. I have talked about these from a perspective that will be relevant for the present dicussion earlier in the article "Emergence form the superpoint" https://www.physicsforums.com/insights/emergence-from-the-superpoint/ . In two or three further installments here we will see how it all comes together and how the higher prequantization of super-p-branes works and what it tellsus about brane charge quantization conditions in string/M-theory.
Sorry, I don't get the joke. Too abstract.

EDIT: I am just kidding with you, Urs.
 
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Hi. This entails too many fancy mathematical and conceptual steps from quantum to classical to prequantum...nature must be simpler! Gerard 't Hooft thinks the basic building blocks of physics are just cellular automata and the rest (Relativity and QM) unnecessary baggage - although he did not spell it out in so many words!
http://arxiv.org/abs/1405.1548
Although the level of my physics is primitive as compared to G 't H's , I agree and have a speculative TOE based on spinning spherically-symmetric Bloch sphere type cellular automata. Beautiful Universe (2005)
http://vladimirtamari.com/beautiful_univ_rev_oct_2011.pdf
Cheers
Vladimir Tamari
 

Urs Schreiber

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nature must be simpler!
What appears simple to the macroscopic, wet, warm and untrained mind tends to be vastly complex fundamentally. Conversely, what is simple fundamentally, may seem elusive at first. If there is interest here on PhysicsForums, I may continue the series beyond the point of traditional set-based reasoning and explain how from the fundamental point of view of adjoint modal homotopy type theory all the apparent complexity here follows in simple steps from first principles.
 
Urs,

It is an amazing post. Really well written.
Could you also add some examples and some exercises here?

Best,
Vijay
 

Urs Schreiber

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Could you also add some examples and some exercises here?
A good exercise to go through is to check my claim that the old prescription of Dirac for deriving magnetic charge quantization, the one that still survives as the "Dirac string" method, is equivalent to what algebraic topologists call the "clutching construction" for complex line bundles. If you get stuck, see the bachelor thesis here http://ncatlab.org/schreiber/show/bachelor+thesis+Eggertsson
 

Urs Schreiber

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I have added to the text a pointer to CGLW 11 where precisely those higher dimensional WZW models that I keep mentioning as examples for higher prequantization are argued to describe the low energy effective physics of symmetry protected topological phases of matter. Maybe we should have a dedicated article just on this class of examples at some point.
 
I get the impression you are using more mathematical specifics and details than is usual when presenting this material in the context of physics -- is that right?
 

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