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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Inside This Book
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First Sentence:
Abstract - In this first part we consider quantum (super)manifolds as topological spaces locally identified with open sets of some locally convex topological vector spaces built starting from suitable topological algebras, quantum (super)algebras. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
integral bordism groups, admissible integral manifolds, quantum superalgebra, singular bordism groups, variational sequence, following exact commutative diagram, infinity prolongation, quantum manifold, variational cohomology, frozen singularities, sectional topology, following local representation, cofinal subspectrum, vector fiber bundle, weak fibration, wedge axiom, integral characteristic numbers, commutative manifolds, cofibre sequence, quantum frame, following short exact sequence, radical differential ideal, quantum algebra, following canonical isomorphism, covariant quantization Key Phrases - Capitalized Phrases (CAPs): (learn more)
Hopf K-algebra, Noetherian K-algebra, Ill Homz New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Abstract - In this first part we consider quantum (super)manifolds as topological spaces locally identified with open sets of some locally convex topological vector spaces built starting from suitable topological algebras, quantum (super)algebras. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
integral bordism groups, admissible integral manifolds, quantum superalgebra, singular bordism groups, variational sequence, following exact commutative diagram, infinity prolongation, quantum manifold, variational cohomology, frozen singularities, sectional topology, following local representation, cofinal subspectrum, vector fiber bundle, weak fibration, wedge axiom, integral characteristic numbers, commutative manifolds, cofibre sequence, quantum frame, following short exact sequence, radical differential ideal, quantum algebra, following canonical isomorphism, covariant quantization Key Phrases - Capitalized Phrases (CAPs): (learn more)
Hopf K-algebra, Noetherian K-algebra, Ill Homz New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 25
books:
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- Noncommutative Geometry by Alain Connes in Back Matter
- Partial Differential Relations (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge A Series of Modern Surveys in Mathematics) by Mikhael Gromov in Back Matter
- Topological Vector Spaces, Distributions and Kernels (Dover Books on Mathematics) by Francois Treves in Back Matter
- Functional Analysis (Springer Classics in Mathematics) by Kosaku Yosida in Back Matter
- Introduction to Supersymmetry and Supergravity by Peter C. West in Back Matter
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