Quantum mechanics with time-dependent parameters

Abstract

Smooth composite bundles provide the adequate geometric description of classical mechanics with time-dependent parameters. We show that the Berry's phase phenomenon is described in terms of connections on composite Hilbert space bundles.

7 pages, LaTeX

References in corpus (2)

• Nonholonomic Constraints in Time-Dependent Mechanics
• On the Geodesic Form of Non-Relativistic Dynamic Equations

Cited by in corpus (14)

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• Action-angle coordinates for time-dependent completely integrable Hamiltonian systems
• Non-abelian higher gauge theory and categorical bundle
• Geometric quantization of time-dependent completely integrable Hamiltonian systems
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• Lectures on Differential Geometry of Modules and Rings
• Geometric quantization of completely integrable Hamiltonian systems in the action-angle variables
• Holonomy of a principal composite bundle connection, non-abelian geometric phases and gauge theory of gravity
• Matrix Operator Approach to the Quantum Evolution Operator and the Geometric Phase
• Axiomatic classical (prequantum) field theory. Jet formalism
• Holonomic control operators in quantum completely integrable Hamiltonian systems
• Geometric phases in quantum control disturbed by classical stochastic processes
• Fibre bundle formulation of time-dependent mechanics
• Covariant geometric quantization of non-relativistic Hamiltonian mechanics