Geodesic
Ghost number and ghost conjugation operators in~the formalism of~BRST quantization
Teoretičeskaâ i matematičeskaâ fizika, Tome 80 (1989) no. 1, pp. 3-14

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Detailed and rigorous study is made of operators of the ghost number $Q_c$ and ghost conjugation $U_c$ which are operators in Krein spaces arising in the BRST quantization formalism for constrained dynamical systems. A number of conditions are obtained which guarantee that $Q_c$ is well-defined and $J$-symmetric. It is shown that properties of $Q_c$ are related to the following geometrical problem: to find conditions under which a pair of lineals in the Krein space can be made neutral by the appropriate choice of $J$-metrics. The complete solution of this problem is given. Whole series of examples is constructed which demonstrate the connections between properties of $Q_c$ and geometry of its spectral subspaces. 
@article{TMF_1989_80_1_a0,
     author = {T. Ya. Azizov and S. S. Horuzhy},
     title = {Ghost number and ghost conjugation operators in~the formalism {of~BRST} quantization},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {3--14},
     publisher = {mathdoc},
     volume = {80},
     number = {1},
     year = {1989},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1989_80_1_a0/}
}
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T. Ya. Azizov; S. S. Horuzhy. Ghost number and ghost conjugation operators in~the formalism of~BRST quantization. Teoretičeskaâ i matematičeskaâ fizika, Tome 80 (1989) no. 1, pp. 3-14. http://geodesic.mathdoc.fr/item/TMF_1989_80_1_a0/