Renormalisation and the Batalin-Vilkovisky formalism
Jun, 2007Citations per year
Abstract: (arXiv)
This paper gives a way to renormalise certain quantum field theories on compact manifolds. Examples include Yang-Mills theory (in dimension 4 only), Chern-Simons theory and holomorphic Chern-Simons theory. The method is within the framework of the Batalin-Vilkovisky formalism. Chern-Simons theory is renormalised in a way respecting all symmetries (up to homotopy). This yields an invariant of smooth manifolds: a certain algebraic structure on the cohomology of the manifold tensored with a Lie algebra, which is a 'higher loop' enrichment of the natural Lie-infinity structure.- quantization: Batalin-Vilkovisky
- gauge field theory: Yang-Mills
- renormalization
- operator: differential
- fibre bundle
- Chern-Simons term
- cohomology
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