Efficient evaluation of real-time path integrals

• URL: http://arxiv.org/abs/2501.16323v1
• Date: Mon, 27 Jan 2025 18:57:04 GMT
• Title: Efficient evaluation of real-time path integrals
• Authors: Job Feldbrugge, Joshua Y. L. Jones,
• Abstract summary: We propose an efficient method for the numerical evaluation of the real-time world-line path integral for theories where the potential is dominated by a quadratic at infinity. Our method directly applies to problems in quantum mechanics, the word-line quantization of quantum field theory, and quantum gravity.
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• Abstract: The Feynman path integral has revolutionized modern approaches to quantum physics. Although the path integral formalism has proven very successful and spawned several approximation schemes, the direct evaluation of real-time path integrals is still extremely expensive and numerically delicate due to its high-dimensional and oscillatory nature. We propose an efficient method for the numerical evaluation of the real-time world-line path integral for theories where the potential is dominated by a quadratic at infinity. This is done by rewriting the high-dimensional oscillatory integral in terms of a series of low-dimensional oscillatory integrals, that we efficiently evaluate with Picard-Lefschetz theory or approximate with the eikonal approximation. Subsequently, these integrals are stitched together with a series of fast Fourier transformations to recover the lattice regularized Feynman path integral. Our method directly applies to problems in quantum mechanics, the word-line quantization of quantum field theory, and quantum gravity.

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