Quantized Partial Differential Equations

By: Agostino Prastaro

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Hardcover | 8 April 2004

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500 Pages

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23.3 x 15.9 x 3

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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.

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Noncommutative manifolds	p. 1
Algebraic topology	p. 1
Quantum algebras	p. 44
Quantum manifolds	p. 63
Quantum supermanifolds	p. 88
Noncommutative PDE's	p. 103
Quantum PDE's	p. 103
The quantum Navier-Stokes equation	p. 121
Quantum super PDE's	p. 132
The quantum super Yang-Mills equations	p. 143
Quantizations of commutative PDE's	p. 193
Integral (co)bordism groups in PDE's	p. 193
Algebraic geometry of PDE's	p. 249
Spectral measures of PDE's	p. 282
Quantizations of PDE's	p. 311
Covariant and canonical quantizations of PDE's	p. 320
Bordism groups and the (NS)-problem	p. 377
Geometry and existence theorems for (NS)	p. 381
Navier-Stokes boundary value problems	p. 390
The limit case : the Euler equation	p. 431
Bordism groups and variational PDE's	p. 435
Horizontal and vertical forms on PDE's	p. 436
The category of variational PDE's	p. 437
Constrained variational sequences	p. 447
Table of Contents provided by Blackwell. All Rights Reserved.

Quantized Partial Differential Equations

At a Glance

Hardcover

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