Higher-order BRST and anti-BRST operators and cohomology for compact Lie algebras | Zendy

Chryssomalis Chryssomalakos | Zendy; J. A. de Azcárraga | Zendy; Alan Macfarlane | Zendy; J C Pérez Bueno | Zendy

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Higher-order BRST and anti-BRST operators and cohomology for compact Lie algebras

Author(s) -

Chryssomalis Chryssomalakos,

J. A. de Azcárraga,

Alan Macfarlane,

J C Pérez Bueno

Publication year - 1999

Publication title -

journal of mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.708

H-Index - 119

eISSN - 1089-7658

pISSN - 0022-2488

DOI - 10.1063/1.533067

Subject(s) - brst quantization , mathematics , pure mathematics , cohomology , order (exchange) , casimir element , laplace operator , operator (biology) , lie algebra , algebra over a field , adjoint representation , mathematical physics , algebra representation , mathematical analysis , gauge theory , cellular algebra , repressor , gene , transcription factor , economics , biochemistry , chemistry , finance

After defining cohomologically higher order BRST and anti-BRST operators for a compact simple algebra {\cal G}, the associated higher order Laplacians are introduced and the corresponding supersymmetry algebra $\Sigma$ is analysed. These operators act on the states generated by a set of fermionic ghost fields transforming under the adjoint representation. In contrast with the standard case, for which the Laplacian is given by the quadratic Casimir, the higher order Laplacians $W$ are not in general given completely in terms of the Casimir-Racah operators, and may involve the ghost number operator. The higher order version of the Hodge decomposition is exhibited. The example of su(3) is worked out in detail, including the expression of its higher order Laplacian W

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