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Mathematical methods in classical mechanics, classical and quantum field theory, quantum mechanics, statistical mechanics, condensed matter, nuclear and atomic physics.
2
votes
Importance of a Hamiltonian integrable system be a bi-Hamiltonian system?
While José's comment pretty much answers this, let me add that, sometimes, it can be hard or impossible to have the system of commuting symmetries $f_j$ under control, and the bihamiltonian recursion …
3
votes
Accepted
Gromov-Witten invariant $\langle p, p, \ell\rangle_{0, 1}$ counting degree $1$, genus $0$ cu...
As Dan says, you can use the divisor equation:
$$\langle e_{\alpha_1}, \ldots, e_{\alpha_n}, \ell \rangle_{g,d} = d\ \langle e_{\alpha_1}, \ldots, e_{\alpha_n} \rangle_{g,d} $$
where the $e_{\alpha_ …
3
votes
Accepted
Toda Hierarchy and Quantum Cohomology of $\mathbb{P}^1$ Frobenius manifolds
I would say that basically everything you wrote is correct, and in particular the equation $F=\lim_{\epsilon\to 0} \epsilon^2 \log \tau|_{t^{\alpha,p>0}=0,t^{\alpha,0}=t^\alpha}$.
It is true that, mor …
5
votes
0
answers
273
views
Deformation quantization of Poisson bracket without star-product
Kontsevich's formality theorem implies in particular that star-products on a $C^\infty$-manifold $M$,
$$f\star g = fg + \sum_{k\geq1} \hbar^k B_k(f,g),\qquad f,g\in C^\infty(M),$$ where $B_k$ are bidi …