Schwinger-Keldysh path integral for the quantum harmonic oscillator

Yoni BenTov

Schwinger-Keldysh path integral for the quantum harmonic oscillator

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arxiv 2102.05029 v1 pith:MRXJU6ZO submitted 2021-02-09 hep-th cond-mat.stat-mech

Yoni BenTov This is my paper · ORCID

classification hep-thcond-mat.stat-mech

keywords pathintegralfunctionalharmonicoscillatorschwinger-keldyshaccommodateassociated

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abstract

I review the generating function for quantum-statistical mechanics, known as the Feynman-Vernon influence functional, the decoherence functional, or the Schwinger-Keldysh path integral. I describe a probability-conserving $i\varepsilon$ prescription from a path-integral implementation of Lindblad evolution. I also explain how to generalize the formalism to accommodate out-of-time-ordered correlators (OTOCs), leading to a Larkin-Ovchinnikov path integral. My goal is to provide step-by-step calculations of path integrals associated to the harmonic oscillator.

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