Abstract
It is known that because of infrared divergence a free massless scalar field in two-dimensional space-time cannot be consistently quantized in a positive-difinite Hilbert space. It is shown that this difficulty can be overcome in the framework of the indefinite-metric quantum field theory. The positivity condition is recovered in a relativistically invariant physical subspace. Various properties of the free massless scalar field are studied in detail as the preliminaries for the investigation of the Thirring and Schwinger models.
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