The Gozzi-Reuter-Thacker path integral for classical mechanics is recovered as a gauge-fixed one-dimensional AKSZ sigma model with target T*(T[1]M × R[1]).
Geometric Dequantization
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abstract
Dequantization is a set of rules which turn quantum mechanics (QM) into classical mechanics (CM). It is not the WKB limit of QM. In this paper we show that, by extending time to a 3-dimensional "supertime", we can dequantize the system in the sense of turning the Feynman path integral version of QM into the functional counterpart of the Koopman-von Neumann operatorial approach to CM. Somehow this procedure is the inverse of geometric quantization and we present it in three different polarizations: the Schroedinger, the momentum and the coherent states ones.
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Reframing classical mechanics: An AKSZ sigma model perspective
The Gozzi-Reuter-Thacker path integral for classical mechanics is recovered as a gauge-fixed one-dimensional AKSZ sigma model with target T*(T[1]M × R[1]).