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We analyze the problems with the so called gauge invariant quantization of the anomalous gauge field theories originary due to Faddeev and Shatashvili (FS). Our analysis bring to a generalization of FS method which allows to construct a series of classically equivalent theories which are non equivalent at quantum level. We prove that these classical theories are all consistent with the BRST invariance of the original gauge symmetry with suitably augmented field content. As an example of such adoi:10.1103/physrevd.54.7664 pmid:10020780 fatcat:bb65klkd2vfszkv6uklnmvwawe