Number theory in Physics

Question

As a Graduate Mathematics student, my interests lies in Number theory. I am curious to know if Number theory has any connections or applications to physics. I have never even heard of any applications of Number theory to physics. I have heard Applications of linear algebra and analysis to many branches of physics, but not number theory.

Waiting forward in receiving interesting answers!

This post imported from StackExchange Physics at 2014-03-24 09:18 (UCT), posted by SE-user Chandrasekhar

Comments

As if the Riemann Zeta function wasn't already cool enough, it has plenty of applications to physics. The temperature at which matter changes phase to be a Bose-Einstein condensate uses $\zeta(3/2)$ in its calculation. Also, this may be of interest: en.wikipedia.org/wiki/Riemann_zeta_function#Specific_values

This post imported from StackExchange Physics at 2014-03-24 09:18 (UCT), posted by SE-user TreyK

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@WaqarAhmad: That's not really physics - it's more of engineering.

This post imported from StackExchange Physics at 2014-03-24 09:18 (UCT), posted by SE-user Sanath Devalapurkar

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Huh, why is mathematical physics a category, is it not part of theoretical physics? They used this tag on TP too, and I regularly use it on MO

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@Dilaton I thought that it could deserve it's own category, since it is done from a "mathematican's perspective", not a physicist's, but then a tag could be enough to distinguish it, so OK.  

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@Dilaton Ok, just fixed all the mathematical-physics tagged questions, and have merged the Mathematical Physics category into the Theoretical Physics category. 

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In squirrel cage motors the bars are employed in prime numbers.

This post imported from StackExchange Physics at 2014-03-24 09:18 (UCT), posted by SE-user Waqar Ahmad

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@Dilaton Was the "mp.mathematical-physics" tag added by you? I am removing it, as Mathematical Physics, Theoretical Physics, Experimental Physics, etc., have their own categories. 

Answer 1

I wasn't aware of this until very recently, when i casually read this article about Ramanujan expressions for modular forms (which are a form of holomorphic functions that leave invariant certain lattices, and are extensively studied for their number-theoretic applications). Apparently there is something called "modular black holes" which i don't have the faintest idea what is about, but it mentions that they are thermodynamically close to normal black holes, so they can be used to compute certain scrambling functions of the event horizon degrees of freedom

I would rather have someone provide an authoritative answer mentioning more details about this, as my ramblings are more or less extracted unmodified from the article. I hope someone that really understand about this gets annoyed enough by my answer and provides a real one.

This post imported from StackExchange Physics at 2014-03-24 09:18 (UCT), posted by SE-user lurscher

Answer 2

Quantum chaos has some deep links to the Riemann hypothesis: http://www.ams.org/samplings/math-history/prime-chaos.pdf

This post imported from StackExchange Physics at 2014-03-24 09:18 (UCT), posted by SE-user Johannes

Comments

While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes.

This post imported from StackExchange Physics at 2014-03-24 09:18 (UCT), posted by SE-user EnergyNumbers

Answer 3

Here is a nice article from a news channel:

• http://www.sciencemag.org/content/274/5295/2014.full

This post imported from StackExchange Physics at 2014-03-24 09:18 (UCT), posted by SE-user Chandrasekhar

Comments

Whilst this may theoretically answer the question, it would be preferable to include the essential parts of the answer here, and provide the link for reference.

This post imported from StackExchange Physics at 2014-03-24 09:18 (UCT), posted by SE-user Dimensio1n0

Answer 4

there is a conjecture so called RIEMANN HYPOTHESIS , which have a deep relationship between the roots of the Riemann Zeta function and the eigenvalues of a Hamiltonian

http://arxiv.org/abs/1101.3116

http://findarticles.com/p/articles/mi_m1200/is_7_174/ai_n30887057/

and my humble paper about the subject http://vixra.org/pdf/1007.0005v8.pdf in fact RIEMANN HYPOTHESIS is juts to use WKB to find a Hamiltonian whose eigenvalues are the square of the RIemann zeros (imaginary part) and its FUNCTIONAL DETERMINANT is just the RIemann Xi function

This post imported from StackExchange Physics at 2014-03-24 09:18 (UCT), posted by SE-user Jose Javier Garcia

Answer 5

The 2-volume "Frontiers in Number Theory, Physics, and Geometry", edited by Cartier et al is a great collection of articles.

My other suggestion would be to have a look at this page ("Number Theory and Physics at the Crossroads" workshop held at Banff) - the bottom half of the page lists a significant number of those areas where physics and number theory flourish together.

This post imported from StackExchange Physics at 2014-03-24 09:18 (UCT), posted by SE-user NitinCR