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 TMF, 1992, Volume 91, Number 1, Pages 3–16 (Mi tmf5557)

True BRST symmetry algebra and the theory of its representations

A. V. Voronin, S. S. Horuzhy

V. A. Steklov Mathematical Institute, USSR Academy of Sciences

Abstract: A simple treatment of BRST symmetry is proposed. From the physical point of view, it expresses a symmetry between ghosts and spurions; from the mathematical point of view, the symmetry operations are linear transformations in the superspaee $C_{1,1}$. From this it follows that the true BRST symmetry algebra is $l(1,1)$, the Lie superalgebra of all linear endomorphisms of $C_{1,1}$, which extends the usual BRST algebra of the generators $Q$ and $Q_c$ with two new generators $K=Q^*$ and $R=\{Q,Q^*\}$. The theory of the representations of $l(1,1)$ is developed systematically. The sets of automorphisms and involutions of $l(1,1)$ are described. Decompositions into irreducible and indecomposable components are constructed for large classes of representations, both finiteand infinite-dimensional. Particular attention is devoted to the analysis of the indecomposable representations (in particular, a connection between them and subspaces of the continuous spectrum of the generators is found) and also of the metric properties of the indefinite spaces of the representations. A class of physical representations is identified and described in detail.

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English version:
Theoretical and Mathematical Physics, 1992, 91:1, 327–335

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Citation: A. V. Voronin, S. S. Horuzhy, “True BRST symmetry algebra and the theory of its representations”, TMF, 91:1 (1992), 3–16; Theoret. and Math. Phys., 91:1 (1992), 327–335

Citation in format AMSBIB
\Bibitem{VorHor92} \by A.~V.~Voronin, S.~S.~Horuzhy \paper True BRST symmetry algebra and the theory of its representations \jour TMF \yr 1992 \vol 91 \issue 1 \pages 3--16 \mathnet{http://mi.mathnet.ru/tmf5557} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1182545} \zmath{https://zbmath.org/?q=an:0782.46057|0774.46045} \transl \jour Theoret. and Math. Phys. \yr 1992 \vol 91 \issue 1 \pages 327--335 \crossref{https://doi.org/10.1007/BF01019825} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1992KF26500001} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. S. S. Horuzhy, A. V. Voronin, “A new approach to BRST operator cohomologies: Exact results for the BRST-fock theories”, Theoret. and Math. Phys., 93:2 (1992), 1318–1327
2. A. V. Voronin, S. S. Horuzhy, “Conformal Theories, BRST Formalism and Representations of the Lie Superalgebras”, Proc. Steklov Inst. Math., 228 (2000), 145–157
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