Dual Jet Geometrization for Time-Dependent Hamiltonians and Applications

Mircea Neagu, Alexandru Oană

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English

Springer International Publishing AG
02 September 2023

Cybernetics & systems theory; Differential & Riemannian geometry; Electricity, electromagnetism & magnetism; Mathematical physics; Maths for engineers

Series: Synthesis Lectures on Mathematics & Statistics

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.

By: Mircea Neagu, Alexandru Oană
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: 2022 ed.
Dimensions: Height: 240mm, Width: 168mm,
Weight: 186g
ISBN: 9783031088872
ISBN 10: 3031088875
Series: Synthesis Lectures on Mathematics & Statistics
Pages: 87
Publication Date: 02 September 2023
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

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.

Reviews for Dual Jet Geometrization for Time-Dependent Hamiltonians and Applications

“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)