Symplectic Manifolds, Coherent States and Semiclassical Approximation

Abstract

We describe the symplectic structure and Hamiltonian dynamics for a class of Grassmannian manifolds. Using the two dimensional sphere ($S^2$) and disc ($D^2$) as illustrative cases, we write their path integral representations using coherent state techniques. These path integrals can be evaluated exactly by semiclassical methods, thus providing examples of localisation formula. Along the way, we also give a local coordinate description for a class of Grassmannians.

17 pages, preprint TCD-4-93, UR-1324,ER40685-774

References in corpus (4)

• Two Dimensional Gauge Theories Revisited
• Quantum Hadrondynamics in Two Dimensions
• Cohomological Partition Functions for a Class of Bosonic Theories
• Exact Path Integrals by Equivariant Cohomology

Cited by in corpus (9)

• Localization and Diagonalization: A review of functional integral techniques for low-dimensional gauge theories and topological field theories
• Coherent states, Path integral, and Semiclassical approximation
• Coherent states over Grassmann manifolds and the WKB-exactness in path integral
• Equivariant Localization of Path Integrals
• EXACTNESS IN THE WKB APPROXIMATION FOR SOME HOMOGENEOUS SPACES
• Path integrals for spinning particles, stationary phase and the Duistermaat-Heckman theorem
• Semiclassical dynamics of a spin-1/2 in an arbitrary magnetic field
• Multi-Periodic Coherent States and the WKB-Exactness II ``Non-compact Case and Classical theories Revisited''
• Multi-Periodic Coherent States and the WKB-Exactness