0000000000313314
AUTHOR
Giuseppe Dito
Deformation Quantization: Genesis, Developments and Metamorphoses
We start with a short exposition of developments in physics and mathematics that preceded, formed the basis for, or accompanied, the birth of deformation quantization in the seventies. We indicate how the latter is at least a viable alternative, autonomous and conceptually more satisfactory, to conventional quantum mechanics and mention related questions, including covariance and star representations of Lie groups. We sketch Fedosov's geometric presentation, based on ideas coming from index theorems, which provided a beautiful frame for developing existence and classification of star-products on symplectic manifolds. We present Kontsevich's formality, a major metamorphosis of deformation qu…
The damped harmonic oscillator in deformation quantization
We propose a new approach to the quantization of the damped harmonic oscillator in the framework of deformation quantization. The quantization is performed in the Schr\"{o}dinger picture by a star-product induced by a modified "Poisson bracket". We determine the eigenstates in the damped regime and compute the transition probability between states of the undamped harmonic oscillator after the system was submitted to dissipation.
Une conférence en l’honneur de Masaki Kashiwara
International audience