Dual Jet Geometrization for Time-Dependent Hamiltonians and Applications
2022 ed.
Book Details
Format
Hardback or Cased Book
Book Series
Synthesis Lectures on Mathematics & Statistics
ISBN-10
3031088840
ISBN-13
9783031088841
Edition
2022 ed.
Publisher
Springer International Publishing AG
Imprint
Springer International Publishing AG
Country of Manufacture
GB
Country of Publication
GB
Publication Date
Sep 1st, 2022
Print length
87 Pages
Product Classification:
Cybernetics & systems theoryCybernetics and systems theoryDifferential & Riemannian geometryDifferential and Riemannian geometryElectricity, electromagnetism & magnetismElectricity, electromagnetism and magnetismMathematical / Computational / Theoretical physicsMathematical physicsMaths for engineers
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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.
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.
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