A rigorous path-integral formula for quantum-spin dynamics via planar Brownian motion

Bodmann, Bernhard; Leschke, Hajo; Warzel, Simone

A rigorous path-integral formula for quantum-spin dynamics via planar Brownian motion

Authors

Bodmann, Bernhard

Leschke, Hajo

Warzel, Simone

Description

Adapting ideas of Daubechies and Klauder we derive a continuum path-integral formula for the time evolution generated by a spin Hamiltonian. For this purpose we identify the finite-dimensional spin Hilbert space with the ground-state eigenspace of a suitable Schödinger operator on $L^2({\mathbb{R}}^2)$, the Hilbert space of square-integrable functions on the Euclidean plane ${\mathbb{R}}^2$, and employ the Feynman-Kac-Itô formula.
4 pages, contribution for the Florence path-integral conference proceedings