Any relation between Quantum Chaos and Quantum Field Theory?

[mad mathematician]

A few years ago I took a course on QC from the mathematics department.

But I didn't see a direct connection to QFT, it seems QC is more connected to QM than to QFT.
But I may be wrong I am just a novice here.

Maybe a good title for a PhD dissertation... (now just to fill the details) so much to read and reread... the headaches

 

[pines-demon]

Quantum chaos seems heavily tied to the non-relativistic semiclassical approximations and the single particle picture, going the QFT route seems to be the opposite direction unless you want to rely quantum field theory with classical field theory. Is classically chaotic field theory even a thing?

 

[mad mathematician]

Quantum chaos seems heavily tied to the non-relativistic semiclassical approximations and the single particle picture, going the QFT route seems to be the opposite direction unless you want to rely quantum field theory with classical field theory. Is classically chaotic field theory even a thing?

Maybe.
I am just trying to generalise all these theories.
So do you say that QC doesn't have the notion of many body physics?
There's this lecture:


Though I haven't yet delved into it. I have the book by Stockman to finish reading. (Isn't Stockman the name of the prof who turns into a mutant fly in Ninja Turtles... ).

 

[Morbert]

Maybe a good title for a PhD dissertation... (now just to fill the details) so much to read and reread... the headaches

Like this? https://dspace.mit.edu/handle/1721.1/156658

 

[pines-demon]

Maybe.
I am just trying to generalise all these theories.
So do you say that QC doesn't have the notion of many body physics?
There's this lecture:


Though I haven't yet delved into it. I have the book by Stockman to finish reading. (Isn't Stockman the name of the prof who turns into a mutant fly in Ninja Turtles... ).

My knowledge of quantum chaos is not up to date, I stand corrected. I was having a hard time seeing how you could connect quantum field theory stuff with classicaly chaotic stuff but apparently there is a lot of this when you throw thermal QFT into the mix, see also: https://arxiv.org/pdf/2408.11123

 

[pines-demon]

Check this, seems like a good introduction: http://www.scholarpedia.org/article/Out-of-time-order_correlations_and_quantum_chaos

 

[Demystifier]

Chaos is studied a lot in the context of quantum black holes, which is a part of quantum gravity, which is a kind of QFT.

 

[mad mathematician]

Chaos is studied a lot in the context of quantum black holes, which is a part of quantum gravity, which is a kind of QFT.

You remind me of this subject called loosely Arithmetic Quantum Cosmology; Never had the time to read it.
And I am not sure how much new is it anyways.

Why did Freeman Dyson think that in Quantum Chaos lies the answer to Riemann Hypothesis?
I once asked someone in the mathematics department if one needs to learn QFT before tackling Arithmetic Quantum Chaos, he said one only needs to know QM.
I guess my question is basically, do we have one canonical Quantum theory?
I mean even String theory is a Quantum theory.

Basically if someone shows that a constructive QFT of 3+1 doesn't exist, what consequences will that have on particle physics community?

 

[pines-demon]

You remind me of this subject called loosely Arithmetic Quantum Cosmology; Never had the time to read it.
And I am not sure how much new is it anyways.

Why did Freeman Dyson think that in Quantum Chaos lies the answer to Riemann Hypothesis?
I once asked someone in the mathematics department if one needs to learn QFT before tackling Arithmetic Quantum Chaos, he said one only needs to know QM.
I guess my question is basically, do we have one canonical Quantum theory?
I mean even String theory is a Quantum theory.

Basically if someone shows that a constructive QFT of 3+1 doesn't exist, what consequences will that have on particle physics community?

Maybe Dyson was thinking on the role of the Riemann function and quantum chaos? I know that the Riemann–Siegel formula and the Selberg zeta function are used there for the semiclassical quantization of nonintegrable systems.

 

[Demystifier]

Basically if someone shows that a constructive QFT of 3+1 doesn't exist, what consequences will that have on particle physics community?

They will take even more seriously the view that QFT is just an effective theory, that only makes sense with some cutoff.

 

[Demystifier]

Why did Freeman Dyson think that in Quantum Chaos lies the answer to Riemann Hypothesis?

http://www.scholarpedia.org/article/Riemann_zeros_and_quantum_chaos