Jet Nestruev
Springer International Publishing
2e druk, 2020
9783030456498
Smooth Manifolds and Observables
Specificaties
Gebonden, blz.
|
Engels
Springer International Publishing |
2e druk, 2020
ISBN13: 9783030456498
Rubricering
Onderdeel van serie
Graduate Texts in Mathematics
Levertijd ongeveer 8 werkdagen
Samenvatting
This book gives an introduction to fiber spaces and differential operators on smooth manifolds. Over the last 20 years, the authors developed an algebraic approach to the subject and they explain in this book why differential calculus on manifolds can be considered as an aspect of commutative algebra. This new approach is based on the fundamental notion of observable which is used by physicists and will further the understanding of the mathematics underlying quantum field theory.
Specificaties
ISBN13:9783030456498
Taal:Engels
Bindwijze:gebonden
Uitgever:Springer International Publishing
Druk:2
Inhoudsopgave
Foreword.- Preface.- 1. Introduction.- 2. Cutoff and Other Special Smooth Functions on R^n.- 3. Algebras and Points.- 4. Smooth Manifolds (Algebraic Definition).- 5. Charts and Atlases.- 6. Smooth Maps.- 7. Equivalence of Coordinate and Algebraic Definitions.- 8. Points, Spectra and Ghosts.- 9. The Differential Calculus as Part of Commutative Algebra.- 10. Symbols and the Hamiltonian Formalism.- 11. Smooth Bundles.- 12. Vector Bundles and Projective Modules.- 13. Localization.- 14. Differential 1-forms and Jets.- 15. Functors of the differential calculus and their representations.- 16. Cosymbols, Tensors, and Smoothness.- 17. Spencer Complexes and Differential Forms.- 18. The (co)chain complexes that come from the Spencer Sequence.- 19. Differential forms: classical and algebraic approach.- 20. Cohomology.- 21. Differential operators over graded algebras.- Afterword.- Appendix.- References.- Index.