|
СЕМИНАРЫ |
Семинар отдела геометрии и топологии МИАН «Геометрия, топология и математическая физика» (семинар С. П. Новикова)
|
|||
|
Quantisation ideals, deformations of non-commutative algebras and corresponding Poisson structures А. В. Михайлов University of Leeds |
|||
Аннотация: We propose to reformulate the problem of quantisation, focussing on quantisation of a dynamical system themselves, rather than of their Poisson structures [1,2,3]. We begin with a dynamical system defined on a free associative algebra $\mathfrak{A}={\mathbb C}[[\hbar]]\langle x_1,x_2,\ldots \rangle $ with non-commutative dynamical variables The new approach enables us to define and present first examples of non-deformation quantisations of dynamical systems, i.e. quantum systems that can be presented in the Heisenberg form This talk is based on a joint work (yet in preparation) with Pol Vanhaecke. [1] A.V.Mikhailov. Quantisation ideals of nonabelian integrable systems. Russ. Math. Surv., 75(5):199, 2020. [2] V.M.Buchstaber and A.V.Mihkailov. {K}d{V} hierarchies and the quantum {N}ovikov equations. arXiv:2109.06357. [3] S.Carpentier, A.V.Mikhailov and J.P.Wang. Quantisation of the Volterra hierarchy. Lett. Math. Phys., 112:94, 2022. |