# Tagged Questions

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### R-matrix and S-matrix in QFT

In the study of quantum field theory, one may encounter S-matrix a lot. Recently, in the study of integrability, I encountered R-matrix formulation which I am not familiar with. First of all, the S-...
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### First integrals for a particle in a central-force field

Consider an arbitrary dimension $n>3$. What are the independent first integrals for a particle? The Hamiltonian is $$H = \frac{p^2}{2m} +V (|r|) .$$
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### Is there a way to get the Bethe Roots, that belong to a given eigenvalue of the transfer matrix?

(Quantum) integrable systems, that belong to solutions to the Yang-Baxter-equation, are often solved by the (algebraic) Bethe Ansatz. Solutions to the Bethe-equations lead to the eigenvalues of the ...
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### Chaos and integrability in classical mechanics

An Liouville integrable system admits a set of action-angle variables and is by definition non-chaotic. Is the converse true however, are non-integrable systems automatically chaotic? Are there any ...
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### Every central-force field is integrable, right?

In 3d, there are four independent first integrals, namely, the three components of the angular momentum, and the total energy. So by the Liouville theorem, it is integrable, right?
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### Anomaly polynomial of Hitchin system $\mathcal{N}=2$ 4d SQFT

I would like to ask about mathematical background of this object. So, I am trying to puzzle out with 4d $\mathcal{N}=2$ SQFT. As far as I can gather this theory can be described in terms of ...
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### On open Gromov-Witten invariants of the projective line

apologies in advance in case this is a stupid question. I'm a mathematician interested in mathematical physics, but, again, penetrating the physics literature is not so easy for me. In the ...
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### Is rigid body rotation an integrable problem?

Is there chaos? The configuration space is 3d. There are four constraints, namely, the energy, the three components of the angular momentum. So there are still two degrees of freedom.
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### How does the functional Bethe Ansatz work?

This question is a bit general and less specific. I've understood the algebraic Bethe Ansatz so far, but since we have a completeness problem Sklyanin suggested a different method, the so called ...
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### A nonintegrable quantum system whose classical limit is integrable?

In this discussion: http://chat.stackexchange.com/rooms/4243/discussion-between-arnold-neumaier-and-ron-maimon Arnold Neumaier suggested that there might be a close link between classical and quantum ...
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### Toda equations and surface operator

I would like to know the reason why the equation (14) in the paper by Yamada is called the Toda equation. \left[\frac12\sum_{i=1}^N\left(y_i\frac{\partial}{\partial y_i}-y_{i+1}\frac{\...