zbMATH — the first resource for mathematics

Noether’s variational theorem II and the BV formalism. (English) Zbl 1038.58020
Bureš, Jarolím (ed.), The proceedings of the 22nd winter school “Geometry and physics”, Srní, Czech Republic, January 12–19, 2002. Palermo: Circolo Matemàtico di Palermo. Suppl. Rend. Circ. Mat. Palermo, II. Ser. 71, 115-126 (2003).
The principal aim of the paper is to emphasize and explain the role of Noether’s second theorem in the Batalin-Vilkovisky (BV) formalism for quantization. In Section 2, the infinite jet bundle model for Lagrangian field theory is reviewed and Section 3 explains Noether’s second theorem in that context, as a one-to-one correspondence between gauge symmetries and Noether identities. By way of example, the Poisson sigma model of Cattaneo and Felder is explained in Section 4. It is for this example that the BV formalism is developed in Section 5; it is shown that the ‘anti-ghosts’, which to a large extent distinguish this theory from the BRST approach, appear in duality to the ‘ghosts’ exactly because of the pairing between gauge symmetries and Noether identities. Some further aspects related to the Gerstenhaber-type bracket which appears in the BV formalism are explained in the final sections.
For the entire collection see [Zbl 1014.00011].

58E30 Variational principles in infinite-dimensional spaces
81T13 Yang-Mills and other gauge theories in quantum field theory
Full Text: arXiv