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<p>In this work, we consider a suitable generalization of the Feynman path integral on a specific class of Riemannian manifolds consisting of compact Lie groups with bi-invariant Riemannian metrics. The main tools we use are the Cartan development map, the notion of oscillatory integral and the Chernoff approximation theorem. We prove that, for a class of functions of a dense subspace of the relevant Hilbert space, the Feynman map produces the solution of the Schrödinger equation, where the Laplace–Beltrami operator coincides with the second-order Casimir operator of the group.</p>

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Feynman Path Integrals on Compact Lie Groups with Bi-invariant Riemannian Metrics

  • 期刊论文

  • 发表日期：

    2025年10月1日

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  • N. Drago,
  • S. Mazzucchi,
  • V. Moretti

摘要

In this work, we consider a suitable generalization of the Feynman path integral on a specific class of Riemannian manifolds consisting of compact Lie groups with bi-invariant Riemannian metrics. The main tools we use are the Cartan development map, the notion of oscillatory integral and the Chernoff approximation theorem. We prove that, for a class of functions of a dense subspace of the relevant Hilbert space, the Feynman map produces the solution of the Schrödinger equation, where the Laplace–Beltrami operator coincides with the second-order Casimir operator of the group.