Abstract
Indecomposable representations of the Poincaré group associated to infrared singular field theory models are discussed in the framework of the general theory of the Gupta–Bleuler triplet formulated by Araki. It is shown that the definition of maximal Hilbert space structures, related to the infrared properties of the states of the models, can be exploited to construct representation spaces for the Gupta–Bleuler triplet. The examples of the two-dimensional massless scalar field and of the electromagnetic field in the Landau gauge are discussed. In particular, in the first example, the relation between the Gupta–Bleuler triplet and the algebraic treatment of the massless scalar field is investigated. In the case of electromagnetism, the structure of the representation of the Poincaré group in the Landau gauge is clarified. The explicit form of the corresponding Gupta–Bleuler triplet for the one-particle space of the electromagnetic field is exhibited.
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