Dual Jet Geometrization for Time-Dependent Hamiltonians and Applications (Synthesis Lectures on Mathematics & Statistics) （2022）

Neagu, Mircea/ Oană, Alexandru

Springer International Publishing AG（2022/09発売）

• 製本 Hardcover:ハードカバー版／ページ数 87 p.
• 言語 ENG
• 商品コード 9783031088841
• DDC分類 530.15539

Full Description

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.

Contents

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.