Takano's Theory of Quantum Painleve Equations

Details Takano's Theory of Quantum Painleve Equations Takano's Theory of Quantum Painleve Equations

2008-04-10

arxiv.org/abs/0804.1644v1

Physics

Mathematical Physics

10 pages

Scientific paper

Recently, a quantum version of Painleve equations from the point of view of their symmetries was proposed by H. Nagoya. These quantum Painleve equations can be written as Hamiltonian systems with a (noncommutative) polynomial Hamiltonian. We give a characterization of the quantum Painleve equations by certain holomorphic properties. Namely, we introduce canonical transformations such that the Painleve Hamiltonian system is again transformed into a polynomial Hamiltonian system, and we show that the Hamiltonian can be uniquely characterized through this holomorphic property.

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