Quantized Partial Differential Equations

Forside
World Scientific, 2004 - 485 sider
This book presents, for the first time, a systematic formulation ofthe geometric theory of noncommutative PDE''s which is suitable enoughto be used for a mathematical description of quantum dynamics andquantum field theory. A geometric theory of supersymmetric quantumPDE''s is also considered, in order to describe quantumsupergravity. Covariant and canonical quantizations of (super) PDE''sare shown to be founded on the geometric theory of PDE''s and toproduce quantum (super) PDE''s by means of functors from the categoryof commutative (super) PDE''s to the category of quantum (super)PDE''s. Global properties of solutions to (super) (commutative) PDE''sare obtained by means of their integral bordism groups.
 

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Innhold

Noncommutative Manifolds
1
Noncommutative PDEs
103
Quantizations of Commutative PDEs
193
Bordism groups and the NSproblem
377
Bordism groups and variational PDEs
435
References
461
Index
473
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