Dual Jet Geometrization for Time-Dependent Hamiltonians and Applications

by Mircea Neagu, Alexandru Oana

Overview

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.

Product Details

ISBN-13:	9783031088858
Publisher:	Springer-Verlag New York, LLC
Publication date:	08/31/2022
Series:	Synthesis Lectures on Mathematics & Statistics
Sold by:	Barnes & Noble
Format:	eBook
File size:	8 MB

About the Author

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.

Table of 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.

Editorial Reviews

This monograph is published in a series of books on applied mathematics and statistics for cross-disciplinary professionals, educators, researchers and students. Its style is quite classical … .” (Anatoliy K. Prykarpatsky, zbMATH 1516.37001, 2023)

From the Publisher