Exact Propagator for $SU(N)$ Coherent State
Phillial Oh
TL;DR
This paper develops an exact classical and quantum solution for an $SU(N)$ isospin model on complex projective space, using integrable systems techniques and coherent state path integrals.
Contribution
It introduces a classical integrable model for $SU(N)$ isospin and derives an exact quantum propagator through coherent state path integrals.
Findings
Exact action-angle variables for the classical system
Closed-form quantum propagator expression
Demonstration of integrability and quantization methods
Abstract
We present a classical integrable model of isospin defined on complex projective phase space in the external magnetic field and solve it exactly by constructing the action-angle variables for the system. We quantize the system using the coherent state path integral method and obtain an exact expression for quantum mechanical propagator by solving the time-dependent Schr\"odinger equations.
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Taxonomy
TopicsQuantum Information and Cryptography · Cold Atom Physics and Bose-Einstein Condensates · Quantum Computing Algorithms and Architecture