The Feynman-Kac formula in deformation quantization

• URL: http://arxiv.org/abs/2502.03624v1
• Date: Wed, 05 Feb 2025 21:18:28 GMT
• Title: The Feynman-Kac formula in deformation quantization
• Authors: Jasel Berra-Montiel, Hugo Garcia-Compean, Alberto Molgado,
• Abstract summary: We introduce the Feynman-Kac formula within the deformation quantization program. The ground state energy of any prescribed physical system can be obtained from the limit of the phase space integration of the star exponential of the Hamiltonian operator.
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• Abstract: We introduce the Feynman-Kac formula within the deformation quantization program. Constructing on previous work it is shown that, upon a Wick rotation, the ground state energy of any prescribed physical system can be obtained from the asymptotic limit of the phase space integration of the star exponential of the Hamiltonian operator. Some examples of this correspondence are provided showing a novel and efficient way of computing the ground state energy for some physical models.

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