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Canonical Discretization (discretization as a canonical transformation)

Mathematical Physics & Probability

Speaker: Alexander Turbiner, UNAM, Mexico and ITEP, Moscow
Location: 693 Kerr
Start time: Tue, Mar 5 2002, 3:10PM

New realization of the Heisenberg algebra in terms of finite-difference (translation covariant) and discrete (dilatation covariant) operators is presented. Since it is a realization of deformation type, it can be treated as a quantum analogue of canonical trasformations. Fock space formalism with a notion of spectral problem is introduced. The formalism provides a natural isospectral connection of differential and difference equations and in particular it leaves polynomial eigenfunctions still polynomial ones. (An)harmonic oscillator as well as the Hahn equation are considered in details as examples.

Albert Schwarz is the host.