Synthesis Lectures on Mathematics & Statistics

Neagu, Mircea; Oană, Alexandru

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.

Details

Published by: Springer

Publication Date: 2023-09-02

Format: Paperback

ISBN-13: 9783031088872

DOI: 10.1007/978-3-031-08885-8

Dimensions: 240cm x168cm

Pages: 87