Principles of Quantum Mechanics · Problem 21.16

Path Integrals—II — R. Shankar

Physics — Quantum Mechanics · path-integrals-spin

Problem

Construct the path integral for a spin-

\frac{1}{2}

particle using spin coherent states

|\theta, \phi\rangle

. Show that the action in the path integral is

S = \int \left[\hbar\dot{\phi}\frac{(1-\cos\theta)}{2} - H(\theta, \phi)\right] dt

where the first term is the Berry phase (Wess-Zumino term) and

H(\theta,\phi) = \langle\theta,\phi|H|\theta,\phi\rangle

is the classical Hamiltonian.