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We study chiral vertex operators in the sine-Gordon [SG] theory, viewed as anoff-conformal system. We find that these operators, which would have beenprimary fields in the conformal limit, have interesting and, in some ways,unexpected properties in the SG model. Some of them continue to have scale-invariant dynamics even in the presence of the non-conformal cosineinteraction. For instance, it is shown that the Mandelstam operator for thebosonic representation of the Fermi field does {\it not} develop a mass term inthe SG theory, contrary to what the real Fermi field in the massive Thirringmodel is expected to do. It is also shown that in the presence of thenon-conformal interactions, some vertex operators have unique Lorentz spins,while others do not.Comment: 32 pages, Univ. of Illinois Preprint # ILL-(TH)-93-1

Chiral vertex operators in off-conformal theory: Sine-Gordon example