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28 March 2024
 
  » arxiv » math-ph/9811016

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A rigorous path integral for quantum spin using flat-space Wiener regularization
Bernhard Bodmann ; Hajo Leschke ; Simone Warzel ;
Date 18 Nov 1998
Journal J. Math. Phys. {f 40} 2549-2559 (1999)
Subject Mathematical Physics | math-ph math.MP quant-ph
AffiliationUniversity of Florida), Hajo Leschke and Simone Warzel (Universität Erlangen-Nürnberg
AbstractAdapting ideas of Daubechies and Klauder [J. Math. Phys. {f 26} (1985) 2239] we derive a rigorous continuum path-integral formula for the semigroup generated by a spin Hamiltonian. More precisely, we use spin-coherent vectors parametrized by complex numbers to relate the coherent representation of this semigroup to a suitable Schrödinger semigroup on the Hilbert space $L^2(R^2)$ of Lebesgue square-integrable functions on the Euclidean plane $R^2$. The path-integral formula emerges from the standard Feynman-Kac-Itô formula for the Schrödinger semigroup in the ultra-diffusive limit of the underlying Brownian bridge on $R^2$. In a similar vein, a path-integral formula can be constructed for the coherent representation of the unitary time evolution generated by the spin Hamiltonian.
Source arXiv, math-ph/9811016
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