 QUANTIZED PARTIAL
DIFFERENTIAL EQUATIONS
by A Prįstaro
(University of Roma "La Sapienza", Italy)
This book presents, for the first time, a systematic
formulation of the geometric theory of noncommutative PDE's which is
suitable enough to be used for a mathematical description of quantum
dynamics and quantum field theory. A geometric theory of
supersymmetric quantum PDE's is also considered, in order to
describe quantum supergravity. Covariant and canonical quantizations
of (super) PDE's are shown to be founded on the geometric theory of
PDE's and to produce quantum (super) PDE's by means of functors from
the category of commutative (super) PDE's to the category of quantum
(super) PDE's. Global properties of solutions to (super)
(commutative) PDE's are obtained by means of their integral bordism
groups.
Contents:
- Quantized PDE's I: Noncommutative Manifolds
- Quantized PDE's II: Noncommutative PDE's
- Quantized PDE's III: Quantizations of Commutative PDE's
- Addendum I: Bordism Groups and the (NS)-Problem
- Addendum II: Bordism Groups and Variational PDE's
Readership: Researchers and graduate
students in the fields of partial differential equations,
mathematical physics and theoretical physics.
| 500pp |
Pub. date: Apr 2004 |
|
