Dual Jet Geometrization for Time-Dependent Hamiltonians and Applications
Dual Jet Geometrization for Time-Dependent Hamiltonians and Applications (Synthesis Lectures on Mathematics & Statistics) by Mircea Neagu, Alexandru Oană
English | September 1, 2022 | ISBN: 3031088840 | 99 pages | MOBI | 16 Mb
English | September 1, 2022 | ISBN: 3031088840 | 99 pages | MOBI | 16 Mb
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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