Integrable Systems on Flag Manifold and Coherent State Path Integral

TL;DR

This paper develops integrable models on flag manifolds utilizing their symplectic structure, quantizes them via coherent state path integrals, and derives exact propagators for specific cases.

Contribution

It introduces a novel construction of integrable models on flag manifolds and applies coherent state path integral quantization to obtain explicit propagator formulas.

Findings

Models are non-commutative integrable systems with conserved Casimir invariants.

Exact propagator expressions are derived for special cases.

The approach links symplectic geometry with quantum integrable systems.

Abstract

We construct integrable models on flag manifold by using the symplectic structure explicitly given in the Bruhat coordinatization of flag manifold. They are non-commutative integrable and some of the conserved quantities are given by the Casimir invariants. We quantize the systems using the coherent state path integral technique and find the exact expression for the propagator for some special cases.