The ghost fields and the BV extension for finite spectral triples
نویسندگان
چکیده
After arguing why the Batalin–Vilkovisky (BV) formalism is expected to find a natural description within framework of noncommutative geometry, we explain how this relation takes form for gauge theories induced by finite spectral triples. In particular, demonstrate two extension procedures appearing in BV formalism, that is, initial via introduction ghost/anti-ghost fields and further with auxiliary fields, can be described language geometry using notions triple total triple, respectively. The construction presented detail all U(2)-gauge triples on algebra M2(C). Indications are given extend results U(n)-gauge n > 2.
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2022
ISSN: ['0022-2488', '1527-2427', '1089-7658']
DOI: https://doi.org/10.1063/5.0089795