Dual Jet Geometrization for Time-Dependent Hamiltonians and Applications

ISBN-13: 9783031088872 / Angielski / Miękka / 2023

Mircea Neagu;Alexandru Oană

Opis

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.

Spis treści

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.

O autorze

Mircea Neagu, Ph.D., is an Associate Professor in the Department of Mathematics and Computer Science at the Transylvania University of Brasov. He received his Ph.D. in mathematics from the Polytechnic University of Bucharest.

Alexandru Oană, Ph.D., is a Lecturer in the Department of Mathematics and Computer Science at the Transylvania University of Brasov.  He received his B.S. in mathematics followed by his Ph.D. in differential geometry dependent on higher order accelerations.

Blurb

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.

• Provides interdisciplinary geometric models in differential geometry, analytical mechanics, dynamical systems, electrodynamics, economics, and theoretical and mathematical physics
• Structured in two parts to present both the geometrical theory and the applicative models
• Studies the differential geometry of spaces in which the metric used for measuring changes in function of time and momentum