A variational principle for actions on symmetric symplectic spaces

Abstract

We present a definition of generating functions of canonical relations, which are real functions on symmetric symplectic spaces, discussing some conditions for the presence of caustics. We show how the actions compose by a neat geometrical formula and are connected to the hamiltonians via a geometrically simple variational principle which determines the classical trajectories, discussing the temporal evolution of such ``extended hamiltonians'' in terms of Hamilton-Jacobi-type equations. Simplest spaces are treated explicitly.

28 pages. Edited english translation of first author's PhD thesis (2000)

References in corpus (2)

• On the propagation of semiclassical Wigner functions
• On Weyl Quantization from geometric Quantization

Cited by in corpus (11)

• The Wigner caustic on shell and singularities of odd functions
• Semiclassical Evolution of Dissipative Markovian Systems
• Symbol correspondences for spin systems
• Even Dimensional Improper Affine Spheres
• On Weyl Quantization from geometric Quantization
• Cotangent bundle quantization: Entangling of metric and magnetic field
• Symplectic Microgeometry II: Generating functions
• The Universal Generating Function of Analytical Poisson Structures
• Symplectic Microgeometry IV: Quantization
• Strongly exponential symmetric spaces
• Cotangent Microbundle Category, I