Reframing classical mechanics: An AKSZ sigma model perspective

Abstract

The path-integral re-formulation due to E. Gozzi, M. Regini, M. Reuter and W. D. Thacker of Koopman and von Neumann's original operator formulation of a classical Hamiltonian system on a symplectic manifold $M$ is identified as a gauge slice of a one-dimensional Alexandrov--Kontsevich--Schwarz--Zaboronsky sigma model with target $T^{\ast }(T[1]M\times \mathbb{R}[1])$.

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