The Geometry of Picture Changing Operators

Carlo Alberto Cremonini

The Geometry of Picture Changing Operators

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arxiv 2305.02828 v1 pith:PU4PXG2Y submitted 2023-05-04 math-ph hep-thmath.AGmath.DGmath.MP

Carlo Alberto Cremonini This is my paper · ORCID

classification math-phhep-thmath.AGmath.DGmath.MP

keywords chainchangingcomplexformspcospicturesomeaims

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This note aims at clarifying some mathematical aspects of what is known in Physics as \emph{Picture Changing Operator} (PCO). In particular, we want to show that PCOs are chain maps between the complex of differential forms (or superforms) and the complex of integral forms on a given supermanifold. We comment on the construction of (super)symmetric PCOs in terms of chain homotopies and we provide some physically relevant examples of applications.

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