Abstract
A systematic and rigorous treatment of the massless scalar field in two dimensions is presented by carefully taking into account the maximal (Krein) state space associated to the Wightman functions. This allows a simple and rigorous answer to controversial statements appearing in the literature about the uniqueness of the translation-invariant state, the construction of translation-invariant operators (infrared operators), the scale and special conformal transformations of the fields, the construction of the dual field and the breaking of the Lorentz transformations, and, more generally, the status of symmetry breaking in the model.
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