Indefinite-Metric Quantum Field Theory of General Relativity | Zendy

N. Nakanishi | Zendy

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Indefinite-Metric Quantum Field Theory of General Relativity

Author(s) -

N. Nakanishi

Publication year - 1978

Publication title -

progress of theoretical physics

Language(s) - English

Resource type - Journals

eISSN - 1347-4081

pISSN - 0033-068X

DOI - 10.1143/ptp.59.972

Subject(s) - physics , mathematical physics , general relativity , unitarity , gauge theory , lorentz transformation , covariant transformation , quantum field theory , theoretical physics , classical mechanics , quantum mechanics

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-l\1ills theory to estnblish thL> unitarity of the physical S-matrix.

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