Sheaf models and massless fields
The role of sheaves in twistor theory is investigated and an account of the logical and model theoretic aspects of sheaf theory is given. It is described also how this formalism leads to a new interpretation of the rôle of sheaves in the twistor description of massless fields. The definitions of sheaves and sheaf maps are firstly given and then the massless fields of helicity \(+\!_-n/2 (n=1,2,...)\) are introduced. The basic structural space-time properties of massless fields are expressed in the form of two exact sequences. The first is a resolution of the differential operator appearing in the massless field equations and the second is the expression of massless fields as potentials modulo a gauge freedom. The main emphasis is put on a self-contained exposition of the theory of sheaf models. The notion of a theory and the notion of its models are carefully distinguished. Some examples of mathematical constructions in the sheaf models are given also. Finally, the language and axioms for the theory of massless fields are given in a form suitable for interpretation in sheaf categories. The fields are defined over a complexified Minkowski space and the interpretational structures are related to the formalism of twistor theory. A sheaf model for the theory of massless fields is developed and it is shown that it is related to the twistor description.
scientific article; zbMATH DE number 3850136