The Batalin–Vilkovisky (BV) formalism is a useful framework to study gauge theories.
We summarize a simple procedure to find a a gauge–fixed action in this
language and a way to obtain one–loop anomalies. Calculations involving the antifields
can be greatly simplified by using a theorem on the antibracket cohomology.
The latter is based on properties of a ‘Koszul–Tate differential’, namely its acyclicity
and nilpotency. We present a new proof for this acyclicity, respecting locality and
covariance of the theory. This theorem then implies that consistent higher ghost
terms in various expressions exist, and it avoids tedious calculations.
This is illustrated in chiral W3 gravity. We compute the one–loop anomaly without
terms of negative ghost number. Then the mentioned theorem and the consistency
condition imply that the full anomaly is determined up to local counterterms. Finally
we show how to implement background charges into the BV language in order
to cancel the anomaly with the appropriate counterterms. Again we use the theorem
to simplify the calculations, which agree with previous results
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