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Lorentz invariant distributions supported on the forward light cone. (English) Zbl 0772.46017
“From the introduction of the authors: From the physical point of view, for instance in the quantum theory of the electromagnetic field, it is of interest to give, for any finite-dimensional module \(U\) for the connected Lorentz group \(G\), a description of the space \(\overline {J}(U)\) of all the \(U\)-valued distributions on (the dual of the) Minkowski space-time that are invariant under \(G\) and supported on the closed forward light cone. Lorentz invariant distributions have of course been studied in depth, not only on physical space-time but on the more general space \(\mathbb{R}^{m,n}\) with a quadratic form of signature \((m,n)\). However the case of the vector-valued distributions as well as the situation when their supports are required to be in the forward (as opposed to the full) light cone have not received the emphasis they deserve in the mathematical literature. Our aim here is to consider these two aspects. We restrict ourselves to the case of signature \((1,n)\)”.
Reviewer: J.Wloka (Kiel)

MSC:
46F10 Operations with distributions and generalized functions
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