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Gauge PDE and AKSZ-type Sigma Models
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abstract
A gauge PDE is a natural notion which arises by abstracting what physicists call a local gauge field theory defined in terms of BV-BRST differential (not necessarily Lagrangian). We study supergeometry of gauge PDEs paying particular attention to globally well-defined definitions and equivalences of such objects. We demonstrate that a natural geometrical language to work with gauge PDEs is that of $Q$-bundles. In particular, we demonstrate that any gauge PDE can be embedded into a super-jet bundle of the $Q$-bundle. This gives a globally well-defined version of the so-called parent formulation. In the case of reparameterization-invariant systems, the parent formulation takes the form of an AKSZ-type sigma model with an infinite-dimensional target space.
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Cited by 1 Pith paper
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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]).
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