6533b7dafe1ef96bd126e1ce
RESEARCH PRODUCT
Unitarity of the SoV Transform for the Toda Chain
Karol K. Kozlowskisubject
Nonlinear Sciences - Exactly Solvable and Integrable SystemsIntegrable systemUnitarityMinor (linear algebra)Hilbert spaceSeparation of variablesFOS: Physical sciencesStatistical and Nonlinear PhysicsMathematical Physics (math-ph)Theoretical physicssymbols.namesakeChain (algebraic topology)symbolsQuantum inverse scattering methodExactly Solvable and Integrable Systems (nlin.SI)QuantumMathematical PhysicsMathematicsdescription
The quantum separation of variables method consists in mapping the original Hilbert space where a spectral problem is formulated onto one where the spectral problem takes a simpler "separated" form. In order to realise such a program, one should construct the map explicitly and then show that it is unitary. In the present paper, we develop a technique which allows one to prove the unitarity of this map in the case of the quantum Toda chain. Our proof solely builds on objects and relations naturally arising in the framework of the so-called quantum inverse scattering method. Hence, with minor modifications, it should be readily transposable to other quantum integrable models solvable by the quantum separation of variables method. As such, it provides an important alternative to the proof of the map's unitarity based on the group theoretical interpretation of the quantum Toda chain, which is absent for more complex quantum integrable models.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2014-08-29 | Communications in Mathematical Physics |