| 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 superspaceC
1,1. From this it follows that the true BRST symmetry algebra isl(1, 1), the Lie superalgebra of all linear endomorphisms ofC
1,1, which extends the usual BRST algebra of the generatorsQ andQ
c
with two new generatorsK=Q
* andR={Q,Q
*}. The theory of the representations ofl(1, 1) is developed systematically. The sets of automorphisms and involutions ofl(1, 1) are described. Decompositions into irreducible and indecomposable components are constructed for large classes of representations, both finite-and 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.V. A. Steklov Mathematics Institute, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 91, No. 1, pp. 3–16, April, 1992. |
