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Cohomological resolutions for anomalous Lie constraints. (English) Zbl 1308.81162

Summary: It is shown that the BRST resolution of the spaces of physical states of the systems with anomalies can be consistently defined. The appropriate anomalous complexes are obtained by canonical restrictions of the ghost extended spaces to the kernel of anomaly operator without any modifications of the “matter” sector. The cohomologies of the anomalous complex for the case of constraints constituting a centrally extended simple Lie algebra of compact type are calculated and analyzed in details within the framework of Hodge-deRham-Kähler theory: the vanishing theorem of the relative cohomologies is proved and the absolute cohomologies are reconstructed.

MSC:

81T70 Quantization in field theory; cohomological methods
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
17B81 Applications of Lie (super)algebras to physics, etc.
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