Abstract
Using the proper definition1 of the massless 2D-propagator – depending on an arbitrary ir-scale μ – we check Elitzur’s conjecture on the ir finiteness of O(N)-invariant Green functions. Explicit computations to the second order in the coupling constant show that non-invariant correlators become finite but μ-dependent objects, whereas the correlators of invariant operators, which are possible candidates for “physical” observables, do not depend on the ir-scale.
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