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Can some one provide some resources for understanding semi-classical approximations for Schwinger-Keldysh path integrals. Is there any discussion about instanton (and multi-instanton) (for even single degree of freedom case would help) contributions to these path integrals in literature?

Sunyam
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A recent preprint https://arxiv.org/abs/2211.05746 presents the construction of the Schwinger-Keldysh technique for systems with instantons (for the case of quantum mechanics with one degree of freedom).

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    Please note that if you are the author of the preprint in question, physics.SE policy requires you to clearly disclose that information - it's okay to cite yourself, but it should be made clear that you're citing yourself. – ACuriousMind Apr 09 '23 at 22:04