# Tagged Questions

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### How obtain conserved quantities in integrable models in accordance with Liouville's theorem, via Sklyanin Poisson algebra?

In classical integrable models, in the discrete case we have the Sklyanin algebra, $$\lbrace T_{a}(u),T_{b}(v)\rbrace =[r_{ab}(u,v),T_{a}(u)T_{b}(v)].$$ How to prove that the conserved quantities are ...
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### Connecting global conservation laws to local features of a function

I have a heuristic question about using global constraints of a problem to make local estimates of geometric features of a curve, such as its local slope. Consider a suitably well behaved function ...
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### Noether currents for the BRST tranformation of Yang-Mills fields

The Lagrangian of the Yang-Mills fields is given by  \mathcal{L}=-\frac{1}{4}(F^a_{\mu\nu})^2+\bar{\psi}(i\gamma^{\mu} D_{\mu}-m)\psi-\frac{1}{2\xi}(\partial\cdot A^a)^2+ ...
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### Is the converse of Noether's first theorem true: Every conservation law has a symmetry?

Noether's (first) theorem states that any differentiable symmetry of the action of a physical system has a corresponding conservation law. Is the converse true: Any conservation law of a physical ...
I have a differential equation of the form $\frac{d^2 y}{dt^2} + f(t) \frac{dy}{dt} + g(t) y = 0$ where $f$ and $g$ are known functions of time. Is there a systematic (or otherwise) way of ...
If a system has $N$ degrees of freedom (DOF) and therefore $N$ independent1 conserved quantities integrals of motion, can continuous symmetries with a total of $N$ parameters be found that deliver ...