loop, and a half-integer in general. If this path arises from trivializing the symplectic vector bundle over a periodic orbit of a Hamiltonian vector field on a symplectic manifold or the Reeb vector field on a contact manifold, it is known as the Conley–Zehnder index. It computes the spectral flow of the Cauchy–Riemann-type operators that arise in Floer homology. It appeared originally in the study of the WKB approximation and appears frequently in the study of quantization, quantum chaos trace formulas, and in symplectic geometry and topology. It can be described as above in terms of a Maslov index for linear Lagrangian submanifolds. References V. I. Arnold, Characteristic class entering in quantization conditions, Funktsional'nyi Analiz i Ego Prilozheniya, 1967, 1,1, 1-14, . V. P. Maslov, Théorie des perturbations et méthodes asymptotiques. 1972 Assorted source material relating to the Maslov index. Symplectic geometry Topology of homogeneous spaces Mathematical quantization