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Tagged Questions

7
votes
1answer
268 views

Book on the Three body Problem

Hi all, I am looking for a good book about the famous (infamous perhaps?) three body problem - both theoretical and numerical hardless and accomplishments. can you help? Thanks
6
votes
1answer
684 views

What is Kirillov’s method good for?

I am planing to study Kirillov's orbit method. I have seen Kirillov's method in several branch of mathematics, for instance, functional analysis, geometry, .... Why is this theory …
19
votes
6answers
3k views

Explanations for mathematicians, about the falsifiability (or not) of string theory [closed]

Like many other mathematicians, I think string theory very attractive. This theory has wonderfully influenced many new topics in mathematics (I myself have worked on one of them), …
1
vote
0answers
56 views

A variation of Poisson’s equation in cylindrical coordinates

Our team of undergraduate physicists are familiar with finding numerical approximations to the following Poisson-like PDE central to our plasma research in a torus: $\nabla^2 V = …
3
votes
1answer
112 views

Are Turaev--Viro invariants secretly a discretized path integral?

Turaev--Viro http://www.ams.org/mathscinet-getitem?mr=1191386 defined an invariant of three-manifolds $M$ denoted $TV(M)$, which was subsequently shown by Kevin Walker to coincide …
15
votes
1answer
682 views

What is about nonassociative geometry ?

At the end of a conference given by Alain Connes in 2000 (here is a video in French), a member of the audience asked a question. I transcribed and translated it for you below: A …
0
votes
0answers
49 views

How to understand the matrix behind a Hamiltonian?

thanks to the answers I received to my previous questions, I could derive correctly an elegant partition function for my problem which resembles a second quantized model taking the …
0
votes
1answer
125 views

identifying dual of lie algebra of general linear groups

Is there any reference for the following fact? I am looking for a nice and simple proof. Assume that $G=GL(n,C)$, the group of invertible $n\times n$ matrices with complex entrie …
8
votes
1answer
183 views

Do circular pipes maximize flow rate?

Suppose that $U \subset \mathbb{R}^2$ is nonempty, open, connected and bounded. Consider a Poisseuille flow in the pipe $U \times \mathbb{R}$. That is: a time-independent incompres …
1
vote
0answers
38 views

Is there a maximal finite depth infinite index irreducible subfactor ?

A subfactor $N \subset M $ is irreducible if $N' \cap M = \mathbb{C} $. It's maximal if it admits no non-trivial intermediate subfactors $N \subset P \subset M $. It's cyclic if i …
3
votes
0answers
460 views

The cyclic subfactors theory: a quantum arithmetic ?

Acknowledgment: Thank you to Vaughan Jones who encouraged me to develop this theory by saying : << Your cyclic idea might have potential... see what you can prove about such …
0
votes
0answers
70 views

Semi-Standard Young Tableaux: Do Diagrams for $O(2m)$ combine to Diagrams from $O(2m+1)$?

Let $n_\lambda^K$ be the number all semi-standard Young tableaux of size $K$ with Ferrers diagrams diagram $\lambda$ (i.e. the number of all fillings of $\lambda$ with natural n …
2
votes
2answers
171 views

Generalized basis

In quantum mechanics, people introduce the notion of "continuous basis" (I actually don't know the mathematical denomination of it). It is not a Schauder basis. I would like to kno …
7
votes
2answers
218 views

Hodge decomposition in Minkowski space

This question is motivated by the physical description of magnetic monopoles. I will give the motivation, but you can also jump to the last section. Let us recall Maxwell’s equati …
2
votes
0answers
110 views

Similarity solutions of the imaginary time Benjamin--Ono equation

This problem arose in the course of a theoretical physics project. We seek (complex) solutions of the imaginary time Benjamin--Ono equation $$u_t-iu u_x-iu_{H,xx}=0$$ where $u_H( …

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