This book studies a category of mathematical objects called Hamiltonians, which are dependent on both time and momenta. The authors address the development of the distinguished geometrization on dual 1-jet spaces for time-dependent Hamiltonians, in contrast with the time-independent variant on cotangent bundles. Two parts are presented to include both geometrical theory and the applicative models: Part One: Time-dependent Hamilton Geometry and Part Two: Applications to Dynamical Systems, Economy and Theoretical Physics. The authors present 1-jet spaces and their duals as appropriate fundamental ambient mathematical spaces used to model classical and quantum field theories. In addition, the authors present dual jet Hamilton geometry as a distinct metrical approach to various interdisciplinary problems.
| ISBN: | 9783031088841 |
| Publication date: | 1st September 2022 |
| Author: | Mircea Neagu, Alexandru Oana |
| Publisher: | Springer an imprint of Springer International Publishing |
| Format: | Hardback |
| Pagination: | 78 pages |
| Series: | Synthesis Lectures on Mathematics & Statistics |
| Genres: |
Differential and Riemannian geometry Cybernetics and systems theory Electricity, electromagnetism and magnetism Mathematical physics Maths for engineers |