ISSN (online): 2153-4373 Nonlinear Studies, 104 Snow Goose Ct, Daytona Beach, FL, 3211 USA. arXiv: 1105.0166[math.AT] Our recent results on {\em extended crystal PDE's} are generalized to PDE's in the category $\mathfrak{Q}_S$ of quantum supermanifolds. Then obstructions to the existence of global quantum smooth solutions for such equations are obtained, by using algebraic topologic techniques. Applications are considered in details to the quantum super Yang-Mills equations. Furthermore, our geometric theory of stability of PDE's and their solutions, is also generalized to quantum extended crystal PDE's. In this way we are able to identify quantum equations where their global solutions are stable at finite times. These results, are also extended to quantum singular (super)PDE's, introducing ({\em quantum extended crystal singular (super) PDE's}).
QUANTUM EXTENDED CRYSTAL PDE's / Prastaro, Agostino. - In: NONLINEAR STUDIES. - ISSN 1359-8678. - STAMPA. - 3:18(2011), pp. 447-485.
QUANTUM EXTENDED CRYSTAL PDE's
PRASTARO, Agostino
2011
Abstract
ISSN (online): 2153-4373 Nonlinear Studies, 104 Snow Goose Ct, Daytona Beach, FL, 3211 USA. arXiv: 1105.0166[math.AT] Our recent results on {\em extended crystal PDE's} are generalized to PDE's in the category $\mathfrak{Q}_S$ of quantum supermanifolds. Then obstructions to the existence of global quantum smooth solutions for such equations are obtained, by using algebraic topologic techniques. Applications are considered in details to the quantum super Yang-Mills equations. Furthermore, our geometric theory of stability of PDE's and their solutions, is also generalized to quantum extended crystal PDE's. In this way we are able to identify quantum equations where their global solutions are stable at finite times. These results, are also extended to quantum singular (super)PDE's, introducing ({\em quantum extended crystal singular (super) PDE's}).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
