Dual jet geometrization for time-dependent Hamiltonians and applications
著者
書誌事項
Dual jet geometrization for time-dependent Hamiltonians and applications
（Synthesis lectures on mathematics and statistics）（Synthesis collection of technology）
Springer, c2022
- : hbk
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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.
目次
The dual 1-jet space.- N-linear connections.- h-Normal N-linear connections.- Distinguished geometrization of the time-dependent Hamiltonians of momenta.- The time-dependent Hamiltonian of the least squares variational method.- Time-dependent Hamiltonian of electrodynamics.- The geometry of conformal Hamiltonian of the time-dependent coupled harmonic oscillators.- On the dual jet conformal Minkowski Hamiltonian.
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