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Quantum field theory of Einstein's general relativity is formulated in the indefinite-metric Hilbert space in such a way that asymptotic fields are manifestly Lorentz covariant and the physical S-matrix is unitary. The general coordinate transformation is transcribed into a q-number transformation, called the BRS transformation. Its abstract definition is presented on the basis of the BRS transformation for the Yang-Mills theory. The BRS transformation for general relativity is then explicitly constructed. The gauge-fixing Lagrangian density and the Faddeev-Popov one are introduced in such a way that their sum behaves like a scalar density under the BRS transformation. One can then proceed in the same way as in the Kugo-Ojima formalism of the Yang-Mills theory to establish the unitarity of the physical S-matrix.
N. Nakanishi (Wed,) studied this question.
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