Event
Robert Conte, ENS Cachan, France
Quantum correspondence for Painlev茅 VI
Le vecteur d'onde de la paire de Lax scalaire de Fuchs pour PVI v茅rifie une EDP parabolique lin茅aire d'ordre deux dont les coefficients sont ind茅pendants du champ de PVI (Suleimanov 1994). Son identification 脿 une 茅quation de Schr枚dinger d茅pendant du temps de la m茅canique quantique exigeait toutefois un ordre ad hoc des produits des op茅rateurs position et impulsion. Nous levons cette ambigu茂t茅 en montrant que l'hamiltonian quantique est le quantifi茅 naturel de la d茅riv茅 logarithmique de la fonction tau de Painlev茅 (1906) et non pas de la fonction tau de Chazy (1911) parce que cette derni猫re brise l'invariance par parit茅 d'un des quatre $ heta_j$.
听
The wave vector of the scalar Lax pair of Fuchs for PVI obeys a generalized heat equation whose coefficients are independent of the PVI field (Suleimanov 1994). Its identification to a time-dependent Schr枚dinger equation of quantum mechanics however required an ad hoc ordering of the products of position and impulsion operators. We remove this ambiguity by showing that the quantum Hamiltonian is the natural quantization of the logaritmic derivative of the tau-function of Painlev茅 (1906), not of the tau-function of Chazy (1911) because the latter breaks the parity invariance of one of the four $ heta_j$.
arXiv:1710.04944
听
The wave vector of the scalar Lax pair of Fuchs for PVI obeys a generalized heat equation whose coefficients are independent of the PVI field (Suleimanov 1994). Its identification to a time-dependent Schr枚dinger equation of quantum mechanics however required an ad hoc ordering of the products of position and impulsion operators. We remove this ambiguity by showing that the quantum Hamiltonian is the natural quantization of the logaritmic derivative of the tau-function of Painlev茅 (1906), not of the tau-function of Chazy (1911) because the latter breaks the parity invariance of one of the four $ heta_j$.
arXiv:1710.04944