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• W4387319635 abstract "A gauge PDE is a geometrical object underlying what physicists call a local gauge field theory defined at the level of equations of motion (i.e. without specifying Lagrangian) in terms of Batalin-Vilkovisky (BV) formalism. This notion extends the BV formulation in terms of jet-bundles on the one hand and the geometrical approach to PDEs on the other hand. In this work we concentrate on gauge PDEs equipped with a compatible presymplectic structure and show that under some regularity conditions this data defines a jet-bundle BV formulation. More precisely, the BV jet-bundle arises as the symplectic quotient of the super jet-bundle of the initial gauge PDE. In this sense, presymplectic gauge PDEs give an invariant geometrical approach to Lagrangian gauge systems, which is not limited to jet-bundles. Furthermore, the presymplectic gauge PDE structure naturally descends to space-time submanifolds (in particular, boundaries, if any) and, in this respect, is quite similar to AKSZ sigma models which are long known to have this feature. We also introduce a notion of a weak presymplectic gauge PDE, where the nilpotency of the differential is replaced by a presymplectic analog of the BV master equation, and show that it still defines a local BV system. This allows one to encode BV systems in terms of finite-dimensional graded geometry, much like the AKSZ construction does in the case of topological models." @default.
• W4387319635 created "2023-10-04" @default.
• W4387319635 creator A5071747420 @default.
• W4387319635 date "2023-01-01" @default.
• W4387319635 modified "2023-10-05" @default.
• W4387319635 title "Presymplectic gauge PDEs and Lagrangian BV formalism beyond jet-bundles" @default.
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• W4387319635 doi "https://doi.org/10.1090/conm/788/15822" @default.
• W4387319635 hasPublicationYear "2023" @default.
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