Quantum extended crystal PDE's

zbMATH Open1253.35135arXiv1105.0166MaRDI QIDQ3100041

Publication date: 22 November 2011

Abstract: Our recent results on {em extended crystal PDE's} are generalized to PDE's in the category

m a t h f r a k 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}).

Full work available at URL: https://arxiv.org/abs/1105.0166

zbMATH Keywords

bordism group crystallographic group existence of global solutions of PDEs stability of solutions of PDEs

Mathematics Subject Classification ID

PDEs in connection with quantum mechanics (35Q40) General mathematical topics and methods in quantum theory (81Q99) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Bordism and cobordism theories and formal group laws in algebraic topology (55N22) Other types of cobordism (57R90)