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Bakalov, Bojko; Nikolov, Nikolay M.

Jacobi identity for vertex algebras in higher dimensions. (English) Zbl 1111.17014

J. Math. Phys. 47, No. 5, 053505, 30 p. (2006).
Summary: Vertex algebras in higher dimensions, introduced previously by Nikolov, provide an algebraic framework for investigating axiomatic quantum field theory with global conformal invariance. We develop further the theory of such vertex algebras by introducing formal calculus techniques and investigating the notion of polylocal fields. We derive a Jacobi identity which together with the vacuum axiom can be taken as an equivalent definition of vertex algebra.

Cited in 11 Documents

MSC:

17B69 Vertex operators; vertex operator algebras and related structures
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
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\textit{B. Bakalov} and \textit{N. M. Nikolov}, J. Math. Phys. 47, No. 5, 053505, 30 p. (2006; Zbl 1111.17014)
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