Sheaf models and massless fields
type: Item
instance of: scholarly article
title: Sheaf models and massless fields
zbMATH Open document ID: 0535.58024
DOI: 10.1007/BF02080672
author: Richard Jozsa
published in: International Journal of Theoretical Physics
publication date: 1984-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 53D50
Mathematics Subject Classification ID: 55N30
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 18F20
zbMATH DE Number: 3850136
zbMATH Keywords: sheaf cohomology of twistor space
zbMATH Keywords: structural space-time properties
zbMATH Keywords: massless field equations
zbMATH Keywords: gauge freedom
reviewed by: Gheorghe Zet
MaRDI profile type: Publication
cites work: Q5792923
cites work: Model theory
cites work: Q4133603
cites work: Cohomology and massless fields
cites work: Q3050433
cites work: Q4145861
cites work: Q5509675
cites work: First order categorical logic. Model-theoretical methods in the theory of topoi and related categories
cites work: Q5182330
cites work: Q3719405
cites work: Q3871177
cites work: Complex manifolds and mathematical physics
description: scientific article; zbMATH DE number 3850136