Calculus of Variations on Fibred Manifolds and Variational Physics A Geometrical Approach to Variational Problems in Physics /
This book presents modern variational calculus in mechanics and field theories with applications to theoretical physics. It is based on modern mathematical tools, specifically fibred spaces and their jet prolongations, which operate with vector fields and differential forms on foundational structure...
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| Main Authors: | , , |
|---|---|
| מחבר תאגידי: | |
| פורמט: | אלקטרוני ספר אלקטרוני |
| שפה: | אנגלית |
| יצא לאור: |
Cham :
Springer Nature Switzerland : Imprint: Springer,
2025.
|
| מהדורה: | 1st ed. 2025. |
| סדרה: | Lecture Notes in Physics,
1033 |
| נושאים: | |
| גישה מקוונת: | https://doi.org/10.1007/978-3-031-77408-9 |
| תגים: |
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| 245 | 1 | 0 | |a Calculus of Variations on Fibred Manifolds and Variational Physics |h [electronic resource] : |b A Geometrical Approach to Variational Problems in Physics / |c by Jana Musilová, Pavla Musilová, Olga Rossi. |
| 250 | |a 1st ed. 2025. | ||
| 264 | 1 | |a Cham : |b Springer Nature Switzerland : |b Imprint: Springer, |c 2025. | |
| 300 | |a 1 online resource (XIII, 331 p. 43 illus.). | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 347 | |a text file |b PDF |2 rda | ||
| 490 | 1 | |a Lecture Notes in Physics, |x 1616-6361 ; |v 1033 | |
| 505 | 0 | |a Chapter 1. Introduction -- Chapter 2. Fibred manifolds -- Chapter 3. Vector fields and differential forms -- Chapter 4. Calculus of variations -- Chapter 5. Dynamical forms and the inverse problem -- Chapter 6. Hamiltonian systems -- Chapter 7. Elements of the variational sequences -- Chapter 8. Extension: Geometrical structures for field theories -- Chapter 9. Variational physics -- Chapter 10. Appendix. | |
| 520 | |a This book presents modern variational calculus in mechanics and field theories with applications to theoretical physics. It is based on modern mathematical tools, specifically fibred spaces and their jet prolongations, which operate with vector fields and differential forms on foundational structures. The book systematically explains Lagrangian and Hamiltonian mechanics and field theory, with a focused exploration of the underlying structures. Additionally, it addresses the well-known inverse problem of calculus of variations and provides examples illustrating key variational physical theories. The text is complemented by solved examples from physics and includes exercises designed to help readers master the subject. Aimed at PhD students, postdocs, and interested researchers, this book assumes prior knowledge of mathematical analysis, linear and multilinear algebra, as well as elements of general and theoretical physics for effective engagement with the discussion. | ||
| 588 | |a Print version record. | ||
| 650 | 0 | |a Mathematical physics. | |
| 650 | 0 | |a Elementary particles (Physics). | |
| 650 | 0 | |a Quantum field theory. | |
| 650 | 0 | |a Mathematical optimization. | |
| 650 | 0 | |a Calculus of variations. | |
| 650 | 1 | 4 | |a Mathematical Physics. |
| 650 | 2 | 4 | |a Theoretical, Mathematical and Computational Physics. |
| 650 | 2 | 4 | |a Elementary Particles, Quantum Field Theory. |
| 650 | 2 | 4 | |a Calculus of Variations and Optimization. |
| 700 | 1 | |a Musilová, Pavla. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 700 | 1 | |a Rossi, Olga. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
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| 773 | 0 | |t Springer Nature eBook | |
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| 776 | 0 | 8 | |i Printed edition: |z 9783031774096 |
| 830 | 0 | |a Lecture Notes in Physics, |x 1616-6361 ; |v 1033 | |
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