A panorama on the modern developments of quantizations of PDEs is given. In particular it is emphasized that on the framework of a geometric theory of PDEs, A. Pr\'astaro has given a formulation of canonical quantization of partial differential equations, without assuming that these should be of variational type and/or linear. Furthermore, the generalization of this geometric approach to PDEs in the category of quantum manifolds, given more recently by A. Pr\'astaro, has been considered. Relations with other recent works in noncommutative geometry are given.
Dirac quantization / Prastaro, Agostino. - STAMPA. - (2001), pp. 127-129. [10.1007/978-0-306-48373-8].
Dirac quantization
PRASTARO, Agostino
2001
Abstract
A panorama on the modern developments of quantizations of PDEs is given. In particular it is emphasized that on the framework of a geometric theory of PDEs, A. Pr\'astaro has given a formulation of canonical quantization of partial differential equations, without assuming that these should be of variational type and/or linear. Furthermore, the generalization of this geometric approach to PDEs in the category of quantum manifolds, given more recently by A. Pr\'astaro, has been considered. Relations with other recent works in noncommutative geometry are given.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
