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For a newly proposed Lagrangian of self-dual fields interacting with gauge fields, we cal-culate its one-cocycle condition, i.e. Wess-Zum ino term, and construct its gauge invariant ver-sion. Through canonical quantization we show that the gauge invariant theory in a proper gauge-fixing is equivalent to its gauge noninvarianr version. Moreover, by using the Baralin-Fradkin-Vilkovisky formalism, we point out that the equivalence is gauge independent.
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