I am studying Weinberg Vol 2 and the BV formalism of the gauge theory.

There, the antifields are introduced somewhat out of thin air. I am a little bit confused about their properties.

For example, there must be an antifield corresponding to the gauge boson according to the BV formalism. Then, what is the gauge transformation law of that specific antifield?

Or do I misunderstand the structure of the formalism? Could anyone please clarify?


1 Answer 1

  1. Well, OP's title question is partially a matter of conventions: Usually one only assigns gauge transformations to the original field sector of a gauge theory. E.g. in Yang-Mills theory, that would be gauge and matter fields. So following the standard terminology, the answer is no.

  2. In more detail, in the BRST formulation, the (infinitesimal) gauge transformations are transcribed into a BRST transformation ${\rm s}$ of an extended BRST multiplet of original and auxiliary fields.

  3. In the Batalin-Vilkovisky (BV) formalism, which is a BRST formulation, the BRST transformation ${\rm s}=(S,\cdot)$ is the antibracket with the BV action $S$ in one slot.

  4. In particular, the BRST transformation of an antifield may be non-zero. Keeping in mind that BRST symmetry encodes gauge symmetry, one may argue that this indirectly addresses/is relevant to OP's title question.


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