Dual Jet Geometrization for Time-Dependent Hamiltonians and Applications
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Beschreibung
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 physicsStructured in two parts to present both the geometrical theory and the applicative modelsStudies the differential geometry of spaces in which the metric used for measuring changes in function of time and momentum
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
Autor*in
Mircea Neagu
Themen in »Dual Jet Geometrization for Time-Dependent Hamiltonians and Applications«
Time-dependent Hamiltonian Momentum d-torsions d-curvatures Einstein-like Equations Maxwell-like equations Dual 1-jet Space Adapted Bases Canonical Nonlinear Connection Cartan Canonical Linear Connection
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“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)
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